Substituting mayonaise for vegetable oil

The major difference between butter and oil is that butter is only 80% oil, with the rest being milk solids and water (source). This means that using oil you will lose some of the water content that your cake should have, possibly resulting in a dryer cake. On the plus side, cakes made with oil tend to dry out slower than those made with butter.

The other possible different, but one that is unlikely with a mix I'd think, is that it depends on the method of mixing in your fat. If the butter is to be whipped or creamed while softened this creates a different texture than one you could get with oil or melted butter. Whipped butter or especially butter creamed with sugar provides a network of air bubbles that act as a raising agent during cooking, and the result is a pound cake like crumb. If your recipe calls for melted butter, though, this is not a concern - the result is more like a traditional muffin or quick bread crumb.

Finally, a vegetable oil has a fairly neutral taste. Usually when a vegetable oil is called for, this is desirable. Butter on the other hand has a more interesting flavor. Your cake may be a bit bland without it.

Brownies are bar cookies. Note that the brownies are at the edge of the pan are more cooked, and raised higher: they set before they settle back down.

Baking the brownies in a mini-muffin tin will essentially make each mini-brownie all edge. They will rise and set very rapidly, and then easily over bake.

I would suggest that brownies are not ideal in a mini-muffin tin. Instead, cutting them smaller would be a better solution.

If you do want to try it again, I would suggest:

1. Don't overfill the tins. You don't want the batter more than about 1/2 inch deep; you want about the same depth it would be in the pan for which they are designed.

2. Let the batter sit for about 5-10 minutes after portioning into the muffin tins. This will give some additional time for the sugars to dissolve, and the flour to hydrate since they won't have as much time in the oven. This should help texture and crust development (the shiny crackly top).

3. Reduce or eliminate the chemical leavening. I would experiment with cutting the baking powder by 50% to start.

   There are ways to incorporate air into brownie batter mechanically, by (for example) beating air into the egg-butter-chocolate mixture, but the exact way to approach it would depend on your particular brownie recipe. If you go that route, you can probably completely eliminate the baking powder.

4. Reduce the oven temperature by about 25 F (maybe even 50 F in a second trial, if they still over bake and are too crusty too rapidly) or so, to allow the baking process to slow, and give more time for the mini-brownies to rise and settle.

5. Check them much sooner. Mini-brownies are going to go from not-done to overdone very, very quickly. I would start checking as early as 15 minutes, until you have an expectation. When you can smell the chocolaty aroma is a good time to start checking.

6. Bake only one mini-muffin tray at a time, so that they are even. You don't want shadow effects and changes in oven convection to throw off the baking by having more than one tray in the oven at the same time, although that is more an issue of consistency than it is of the complete character of the outcome.