Preheat and prep: Heat oven to 350°F (175°C). Line a 12-cup muffin tin with cupcake liners.
Set butter for frosting out to soften.
Make the cupcake batter: In a bowl, whisk 1 2/3 cups flour, 1 1/2 teaspoons baking powder, and 1/2 teaspoon fine sea salt. In a separate bowl, beat 1/2 cup melted, slightly cooled unsalted butter with 1/4 cup neutral oil, 3/4 cup granulated sugar, and 1/4 cup light brown sugar until combined. Beat in 2 eggs and 2 teaspoons vanilla.
Add dairy: Mix in 1/3 cup sour cream until smooth.
Add dry ingredients in two additions, alternating with 1/2 cup whole milk. Stir just until combined. Do not overmix.
Fill and bake: Divide batter evenly among liners (about 3/4 full). Bake 18–20 minutes, until tops spring back or a toothpick comes out clean.
Cool in pan 5 minutes, then move to a rack to cool completely.
Make the caramel sauce: In a light-colored saucepan, add 1 cup granulated sugar in an even layer over medium heat. Let it melt, stirring gently as it liquefies and turns amber. Add 1/2 cup heavy cream slowly (it will bubble).
Stir in 1/2 cup unsalted butter, 1/2 teaspoon fine sea salt, and 1 teaspoon vanilla. Simmer 30–60 seconds until smooth. Cool to room temperature; it should be pourable but thick.
Core the cupcakes: Once cooled, use a small knife or cupcake corer to remove a shallow plug from the center of each cupcake.
Save the plugs.
Fill with caramel: Spoon or pipe about 1–2 teaspoons caramel into each hole. Replace a bit of the cupcake plug on top to cover. Reserve some caramel for the frosting and drizzle.
Make salted caramel buttercream: Beat 1 cup room-temperature unsalted butter until creamy, 2–3 minutes. Add 3 cups powdered sugar, 1/4 teaspoon fine sea salt, and 2 tablespoons cooled caramel.
Beat on low until combined, then on high until fluffy, 2 minutes. Add 1–2 tablespoons heavy cream to reach a silky, pipeable consistency. Taste and add more caramel or salt if needed.
Frost the cupcakes: Transfer frosting to a piping bag fitted with a large round or star tip.
Swirl generous mounds on each cupcake.
Finish with flair: Drizzle remaining caramel over the frosting and add a pinch of flaky sea salt. Serve at room temperature.