Preheat the oven to 325°F (160°C). Grease and flour a 10-inch bundt pan, tapping out excess flour.
In a large bowl, cream the softened butter with the brown sugar and granulated sugar until light and fluffy, about 4–5 minutes.
Add the eggs one at a time, mixing well after each addition. Stir in the vanilla extract.
In a separate bowl, whisk together the all-purpose flour, baking powder and salt.
Add the dry ingredients to the butter mixture in three additions, alternating with the sour cream (beginning and ending with the dry ingredients). Mix until just combined; do not overmix.
Pour the batter into the prepared bundt pan and smooth the top. Bake in the preheated oven for 65–75 minutes, or until a toothpick inserted in the center comes out clean.
Let the cake cool in the pan for 10 minutes, then invert onto a wire rack to cool completely.
While the cake cools, make the caramel glaze: combine the brown sugar, heavy cream and butter in a small saucepan over medium heat. Bring to a gentle simmer, stirring constantly, until the sugar dissolves and the mixture thickens slightly, about 3–5 minutes.
Remove from heat and stir in the sea salt and vanilla extract. Allow the glaze to cool until slightly thickened but still pourable.
Pour the warm caramel glaze over the cooled cake, letting it drip down the sides. Slice and serve.
Notes
Store leftover cake covered at room temperature for up to 3 days or refrigerated for up to 5 days. Warm slices briefly before serving for best texture.