Preheat your oven to 350°F (175°C) and generously grease a 10-cup Bundt pan, making sure to coat all the crevices. In a medium bowl, whisk together the flour, baking powder, baking soda, and salt, then set aside. In a large mixing bowl, beat the softened butter, granulated sugar, and brown sugar until light and fluffy, about 3–4 minutes. Add the eggs one at a time, beating well after each addition, then mix in the vanilla extract. With the mixer on low speed, gradually add the dry ingredients to the wet, alternating with the buttermilk—beginning and ending with the dry ingredients. Mix just until everything is fully incorporated; be careful not to overmix. Pour the batter into the prepared Bundt pan and smooth the top. Bake for 35 to 40 minutes, or until a toothpick inserted into the center of the cake comes out clean. Allow the cake to cool in the pan for 15 to 20 minutes, then carefully invert it onto a wire rack to cool completely.

In a heavy-bottomed saucepan, combine the brown sugar, sweetened condensed milk, corn syrup, and salt. Place over medium heat and bring the mixture to a gentle boil, stirring constantly. Let it boil for 4 to 5 minutes, continuing to stir, until the mixture is smooth and thickened. Remove the pan from the heat and add the butter and vanilla extract, stirring until the butter is completely melted and the sauce is glossy and smooth. Drizzle the warm caramel sauce over the cooled cake as desired. Any leftover sauce can be stored in an airtight container in the refrigerator for later use—just reheat gently before serving.