Cream butter: In a mixing bowl, use an electric mixer to cream together softened vegan butter and granulated sugar until light and fluffy. (If working by hand, use a whisk and vigorously beat ingredients until fluffy.)
Add wet ingredients: Add in nondairy yogurt and vanilla extract and blend until combined.
Add dry ingredients: Add in all-purpose flour, baking soda, cream of tartar, and salt. Blend together on a low speed until about 80% combined. Then switch to a rubber spatula and finish folding ingredients together. (This will help to avoid over-mixing.)
Chill dough: Cover the dough and refrigerate for at least 30 minutes, or up to 3 days.
Prep for baking: When the dough is almost done chilling, preheat oven to 350°F. Optionally, line a baking sheet with parchment or a silicone baking mat.
Roll cookies: Roll dough into roughly 1" sized balls. For even portions, I use an OXO Medium Cookie Scoop which measures 1 1/2 tablespoons per cookie. For me this recipe yields 12 cookies of this size.
Coat in cinnamon sugar: Combine cinnamon and sugar in a bowl. Roll each dough ball in cinnamon sugar until evenly coated.
Bake: Bake in preheated oven for 10-12 minutes, or until cookies are puffy and appear set around the edges. For soft cookies, I usually take mine out at 11 minutes. If you prefer slightly crisp edges, you can extend the cook time until you see slight browning around the edges.