Preheat your oven to 350°F (175°C). In a large bowl, cream together the softened salted butter and granulated sugar using an electric mixer until light and fluffy, about 3-4 minutes. Add the eggs one at a time, beating well after each addition. Stir in the vanilla, butter, and rum extracts.

In a separate bowl, whisk together the cake flour and baking soda. Gradually add the dry ingredients to the wet mixture, alternating with the sour cream. Begin and end with the flour mixture, mixing just until incorporated. Avoid overmixing to keep the cake tender.

Grease and flour your 9-inch cake pan. Pour the batter evenly into the pan and smooth the top. Bake in the preheated oven for about 40-45 minutes, or until a toothpick inserted in the center comes out clean. Remove from oven and allow the cake to cool in the pan for 15 minutes, then transfer to a wire rack to cool completely.

In a medium saucepan over medium heat, melt the 6 tablespoons of salted butter. Add the sugar and stir constantly until it dissolves and turns a deep amber color. Carefully whisk in the heavy cream (it will bubble up), then add the kosher salt. Stir until smooth and remove from heat. Let the glaze cool slightly until it thickens but is still pourable.

Once the cake is fully cooled, pour the salted caramel glaze evenly over the top, letting it drip down the sides naturally. Sprinkle with flaky sea salt to enhance the caramel flavor and add a beautiful finish.

Allow the glaze to set for about 15 minutes before slicing. Serve your salted caramel butter cake as a decadent dessert with a cup of coffee or tea.