Combine all-purpose flour, soy protein powder, and oat flour together in a bowl.
Beat white sugar, brown sugar, yogurt, and butter together in a large bowl with an electric mixer until smooth and creamy. Add vanilla extract. Stir in flour mixture. Mix in milk, 1 tablespoon at a time, until batter is thick and smooth. Fold in chocolate chips.
Roll batter into 1-inch balls with your hands. Arrange on a baking sheet. Transfer to the freezer and chill until firm, about 1 hour, or in the refrigerator, 2 to 3 hours.