Preheat oven to 325°F (170°C).
In the bowl of a stand mixer fitted with the paddle attachment, beat softened butter, ½ cup (100 grams) granulated sugar, and ¼ cup (55 grams) brown sugar at medium speed until fluffy, 2 to 3 minutes, stopping to scrape sides of bowl. Add eggs, one at a time, beating well after each addition. (Mixture may look slightly curdled, but batter will come together.)
In a medium bowl, whisk together flour, baking powder, salt, and baking soda. In a small bowl, whisk together yogurt, milk, and vanilla. With mixer on low speed, gradually add flour mixture to butter mixture alternately with yogurt mixture, beginning and ending with flour mixture, beating just until combined after each addition. (Batter will be thick.)
Spray a 6-well Bundlette pan with baking spray with flour. Using a pastry brush, spread any excess spray in pan, blotting brush with a paper towel as needed. (See Note.) Spoon about ½ cup (about 110 grams) batter into each prepared well. Tap pan on a kitchen towel-lined counter several times to spread batter into grooves and release any air bubbles.
Bake until a wooden pick inserted near center comes out clean and an instant-read thermometer inserted near center registers 205°F (96°C), 17 to 20 minutes. Let cool in pan for 10 minutes. Invert cakes onto a wire rack placed over a rimmed baking sheet, and let cool completely.
In another small bowl, stir together cinnamon, remaining ¼ cup (50 grams) granulated sugar, and remaining 2 tablespoons (28 grams) brown sugar. Brush melted butter onto cooled cake, and cover with cinnamon mixture, gently pressing to adhere. Place cakes on desired serving dishes.
Spoon dulce de leche into a pastry bag fitted with a ½-inch open star piping tip (Ateco #824), and pipe into center of cakes. Refrigerate in an airtight container for up to 3 days.