Most desserts are vegetarian (unless gelatin is involved--since it comes from dead animals, I don't consider it vegetarian) but vegan desserts are surprisingly easy.  This is probably because the crucial dessert ingredients are sugars, not fat.  Naturally, some vegan desserts can be fat free too.  The main tip is to realize the butter and egg can be substituted for mashed banana, applesauce, or canned pumpkin (applesauce has the most invisible taste and is recommended when you don't want the substitute competing with another flavor).  I generally recommend adding applesauce last so you can reach the consistency you want depending on the type of dessert.  Theoretically, peanut butter (or sun butter or pumpkin butter or any nut butter you can think of) should be able to replace butter in recipes since it adds protein and fat, but I've never tried it since it's fattening, adds a strong flavor, and there are more convenient substitutes.  For cake icing, I recommend using the same amount of vegetable oil as you would butter.  Keep in mind that it is the nature of desserts to add pounds or give you diabetes.  Here's a cookie recipe to get people started.  If anyone else has recipes, please share.

1 teaspoon vanilla extract

1 mashed banana (can be substituted with equivalent applesauce or pumpkin--pumpkin works well if it's a thanksgiving dessert)

3/4 cup plus 2 tablespoons all-purpose flour, or as needed

1/2 teaspoon baking soda

1/4 teaspoon salt

1/4 teaspoon ground cinnamon

2 cups quick-cooking (not instant) oatmeal or rolled oats

1/2 cup chopped walnuts

1/2 cup raisins*¹

1. Preheat oven to 350 degrees. Lightly spray two baking sheets with oil. In a mixing bowl, mash banana well. Add  sugar and vanilla, and mix with a strong fork. Add flour, baking soda, salt and cinnamon, and mix until just moistened.

2. Add oatmeal, walnuts and raisins. Using your hands or a sturdy spoon, mix well, making sure oats are well moistened. (If dough is very slippery, add one or two extra tablespoons flour.)

3. Using clean, wet hands, re-wetting as needed, roll dough into balls slightly smaller than a golf ball, about 1 1/3 inches in diameter. Flatten slightly and place 2 inches apart on a baking sheet. Bake until lightly browned, 10 to 12 minutes. Remove from heat and allow to cool for 2 minutes, then transfer to a rack to cool completely. Store in an airtight container

*¹ the recipe originally called for chocolate chips, and if you can find vegan chocolate chips go for it

*^{2 the oil was also originally called for, but I found it unnecessary to reach the desired consistency--if there are still dry ingredients feel free to add some (the recipe called for 1/3 of a cup)}

Good luck