You can do it sans machine, but you are limited to small batches, and it tends to form crystals. You have two choices, bags or freezer container. Bags tends to make less crystallized product, and is a bit faster.
Bags
Get a large 1 gallon ziploc bag, lots of ice, a ~2 cups salt, a small, 1 quart bag and the mix to be turned into ice cream (or frozen yogurt). Chill the mix in the fridge beforehand. This helps the mix cool more quickly and evenly, meaning smaller crystals, meaning creamier product.
Place the cream mix in the small bag, and leave a bit of air. Make sure it is sealed well, you may want to double bag it. Put the small bag in the big bag.
Fill the big bag about half way with ice and add a few tablespoons of salt. Seal the big bag and start mushing the small bag from outside the big bag, moving it around and getting it in contact with the ice. You probably want gloves or to wrap it in a towel: it gets really cold. After the ice melts down, add more ice and salt, keep squishing until the stuff in the bag gets hard. You can toss it on the floor and squish it with your feet while watching TV or reading. Put it in the freezer for a few hours to condition.
This isn't quite as nice as a machine. To compensate for the extra crystallization, you can add more fat and sugar, since those stop large crystals from forming. With frozen yogurt, I don't think there is much you can do.
Freezer Container
This is easier, but makes lower quality product. Simply put your mix in a large container (leave at least half empty), and place in the freezer. Take it out every 10 minutes and shake vigorously for a few seconds. Repeat until it won't move anymore. Use a fork to fluff the mix.
Frozen yogurt made with full fat yogurt is very creamy and full flavored. You might find that the eggs are unnecessary.
If you do do the custard watch you temperature carefully as yogurt curdles easily when it is heated. If you have a lot of fat in the yogurt then it will be resistant to curdling otherwise you can take out some insurance by mixing in a little bit of corn starch- if that is allowed.
Honey is perfectly fine and many frozen yogurt recipes call for it.
Best Answer
Actually, the yogurt cultures, usually some strain of the group N Streptococcus and Leuconostoc species, mesophilic cultures, converts the lactose into lactic acid, which gives the diary product it's tart taste.
Furthermore, bacterial enzymes transform the milk carbohydrates into oligosaccharides, some of which have prebiotic properties.
Different LAB (Lactic Acid Bacteria) produce different fermentation products, although they have in common that they are alive in the product and can interact with microbiota during intestinal transit and the cells of the intestinal wall.
Fermentation of soy milk with lactic acid bacteria offers a means of preserving soy milk and the possibility of modifying the characteristic flavor and texture to make it more acceptable to Western taste.
It is possible to make soy milk yogurt-like products with acceptable texture and clean acid flavor. The choice of fermenting organisms is limited to those that can ferment the sugars typical of soy milk. i.e. stachyose. raffinose or sucrose. unless sugars fermented by the desired cultures are added to the soy milk.
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