Preheat oven to 375°F and lightly grease a mini muffin pan or line with mini liners. In a medium mixing bowl, whisk together the flour, baking powder, and baking soda until evenly combined. In a separate mixing bowl, whisk together the dairy-free yogurt and sugar until smooth. Add the melted (slightly cooled) butter, applesauce, and vanilla extract, mixing until fully combined and creamy. Pour the dry ingredients into the wet ingredients and gently mix until just combined. The batter should be thick, avoid overmixing to keep the muffins soft.
Fold in the sprinkles, distributing them evenly throughout the batter without overworking it.
Scoop the batter into the mini muffin pan, filling each cavity about ¾ full for even baking. Bake for 12–14 minutes, or until the tops are set and a toothpick inserted into the center comes out clean or with a few soft crumbs.
Let the muffins cool in the pan for 5 minutes, then transfer to a wire rack to cool completely. This helps them set while staying soft and fluffy.