Preheat the oven to 350°F. Line a 9-inch square pan with parchment, leaving an overhang, and lightly spray it. A tall-sided 8-inch square pan may be used for a thicker cake.

Brown 1/2 cup unsalted butter in a small saucepan until nutty and golden. Cool 5 minutes. Stir in 1 cup flour, 1/2 cup light brown sugar, 1 teaspoon cinnamon, 1/4 teaspoon fine sea salt, 1 teaspoon vanilla, and 1/2 cup chopped pecans until clumpy. Set aside.

Warm 1 cup thick caramel with 1 tablespoon milk in short microwave bursts, stirring until smooth. Stir in 1/4 teaspoon flaky salt if using. Cool briefly until thick but drizzleable.

Whisk 2 cups flour, 1 cup sugar, 1 teaspoon baking soda, 1 teaspoon baking powder, 1/2 teaspoon fine sea salt, and 1 teaspoon cinnamon in a large bowl. In another bowl, whisk 1 cup sour cream or plain Greek yogurt, 2 eggs, 1/2 cup melted unsalted butter, and 2 teaspoons vanilla. Fold the wet ingredients into the dry ingredients just until combined.

Spread half the batter in the prepared pan. Drizzle with half the caramel and swirl lightly. Add the remaining batter, drizzle with the remaining caramel, and swirl lightly again. Scatter all the brown butter pecan streusel over the top.

Bake at 350°F for about 35 to 45 minutes in a 9-inch pan, or about 40 to 50 minutes in a deeper 8-inch pan. The center should be set, and a toothpick inserted into cake crumb away from caramel should show no wet batter. Cool in the pan for at least 20 minutes, then finish with a pinch of flaky sea salt if desired and cut into 12 slices.