Preheat your oven to 375°F and line two baking sheets with parchment paper. Grab your mixer and cream together the softened butter and 1 cup sugar until it's pale and fluffy, about 2 minutes. This step matters because it traps air bubbles that make your snickerdoodle cookies recipe come out tender instead of dense.
Beat in your eggs one at a time, making sure each one fully incorporates before adding the next. Add the vanilla powder and mix until combined. The batter should look smooth and slightly lighter than when you started.
In a separate bowl, whisk together the flour, baking soda, cream of tartar, and salt. Pour the milk into your mixer bowl, then add the dry ingredients in two parts, mixing on low speed. Don't overmix here—stop as soon as you don't see dry flour streaks.
Mix the cinnamon and 1/2 cup sugar together in a shallow bowl and set it aside. Brush the melted butter onto a small plate next to your cinnamon mixture—this is your rolling station.
Scoop dough into 1-tablespoon sized balls (mine always stick a little to the ice cream scoop and that's fine). Roll each ball in melted butter first, then press it into the cinnamon-sugar mixture so it gets totally coated on all sides.
Place your coated dough balls on the prepared baking sheets about 2 inches apart. Here's my secret: don't flatten them! They'll spread on their own, and you want them to puff up during baking.
Bake for 12 minutes until the edges are set but the centers still look slightly underbaked (that's when they stay soft). They'll continue cooking on the hot pan for another minute after you pull them out. Let them cool on the baking sheet for 5 minutes, then transfer to a wire rack.