Well, if air is the only raising agent, simply add less of it by not beating the mixture as much. Failing that, beat as normal, then give the mixing bowl a couple of (careful) bangs on the counter top to knock the air out it again.
A bit of experimentation will be necessary to get the right results, I think: perhaps pour some of the mixture into the tin as is, then knock the air out of the remaining mixture and compare the results.
It depends a lot on what you expect. I wouldn't call it a mess. The result will be edible, and will have a similar flavor to a brownie. The texture will be very different from a brownie. It will be dry and dense. Personally, I wouldn't eat it.
First, the fat plays important roles in baked goods besides taste. I am surprised to see a recipe which uses melted fat (so no creaming) and no baking powder. This thing (the original one) is going to be denser than chewy cookies - maybe OK for you. If you reduce the fat from the original recipe, you will get a very dry result. An airy cake which is dry is not too good, but can be eaten when combined with e.g. yogurt or other wet things. Something which is both dense and dry will taste like chicken food mix run through a dehydrator. If you have a recipe for baking, don't reduce the fat. Also, never use spreads or margarines or anything else which is not real fat. It does not act like real fat, so it doesn't work the way it should. It is likely to contain lots of water and gums, and melt into them when baked. For baking, always use butter, lard or shortening. (It is OK to use vegetable oils for dense recipes which direct you to melt the butter). You will need your full share of fat. Some people replace part of the butter with applesauce, but you can't replace all of it. Also, I don't know how it will act in a non-leavened recipe.
Second, you need the sugar the same way you need the fat. It retains moisture and makes the brownies soft. Honey is already a risky proposition, but partial replacement will work. But do not reduce the sugar by half, it will make dry, unpleasant brownies. Also, I don't know what "no calorie sugar" is, but it sounds like some artificial sweetener dispersed in a filler. I don't know what the filler is made from, but it may not be good for baking.
You can't always replace wheat flour with other flours, but finelly milled oats should work for brownies and cakes.
Using a vegetable or fruit puree in place of the liquid is normally a good substitution, but your recipe doesn't have liquid. Just adding cabbage will destroy the liquid balance. You could theoretically replace part of the eggs with an equal amount of cabbage puree by weight, but because eggs also have important roles in baking (they lubricate and set the dough), you shouldn't nomrally replace them.
So, the replacement will bake into something you can bite and chew and swallow, but I wouldn't call it brownie. It also wouldn't be a tasty non-brownie, at least not in my eyes. Also, if you go ahead and make the stuff, you don't even win much in calories. Your original recipe is about 2950 kcal, and you get 820 g of brownies, resulting in 359 kcal/100 g. Your replacement recipe is 1610 kcal but only 530 g of brownies, which makes it 302 kcal/100 g (still a very caloriedense food) - and that if you use these substitution products, which are bad for baking. So, you only lose 15% of the calories overall, but you get something which tastes nowhere near the original. It will have cocoa flavor, but it won't be moist and creamy. I would rather eat 100 g of real brownies than 115 g of brownies made with your recipe.
Best Answer
Your first method -- beating eggs and sugar "to the ribbon" -- is a process of denaturing some of the egg proteins into a lattice that will help capture steam as the batter bakes. Also, this method helps ensure your eggs will be well distributed in the batter, with no stripes of eggwhite anywhere.
Your second method -- beating sugar and softened butter to a pale yellow -- appears to be the creaming method, which uses sugar granules to punch millions of tiny air bubbles into the butter. By using this method, when the batter bakes, you get a more even "crumb" (texture of the holes in the final cake). Though you did not mention it, typically this method is used with recipes calling for baking powder/baking soda (you can use the method without a chemical leavener). Also, I would expect the butter-sugar creaming step to take place before you add your melted chocolate.
Neither method is inherently necessary; if you simply stir all ingredients together at once into a uniform batter, you will still get a tasty product. That said, each technique will tend to lighten the brownie into a more cake-like texture, rather than a dense, fudge-like texture. You can do both, if you like, by dividing your sugar in half.