Warm milk to 110°F (43°C). Stir in yeast and 1 teaspoon sugar; let foam for 5-10 minutes until puffy.
In a stand mixer with dough hook, combine flour, sugar, salt, and cinnamon. Add yeast mixture, eggs, melted butter, oil, and vanilla. Mix on low until shaggy, then knead on medium for 6-8 minutes until smooth and elastic.
Shape dough into a ball, place in a greased bowl, cover, and let rise in a warm place for 1.5-2 hours until doubled in size.
Beat butter and powdered sugar until creamy. Add vanilla and salt, then mix in flour until a soft cookie-like dough forms. Divide into 12 portions and flatten into 3-inch discs.
Punch down the dough and divide into 12 equal pieces (about 65-70g each). Roll each into a smooth ball and place on parchment-lined baking sheets, 3 inches apart.
Place a topping disc over each dough ball and press gently to adhere. Score with a concha stamp or paring knife to create a seashell or cross-hatch pattern, cutting only through the topping.
Cover loosely and let rise for 40-60 minutes until puffy. Preheat oven to 350°F (175°C) during the last 15 minutes.
Bake for 18-22 minutes until the bottoms are lightly golden. Cool on the pan for 5 minutes, then transfer to a wire rack to set for at least 10 minutes before serving.