Step 1: Preheat your oven to 325°F (160°C). Grease and flour a 10-12 cup Bundt pan or a 10-inch tube pan. Set aside.
Step 2: In a large mixing bowl, using an electric mixer, cream together the softened butter and cream cheese until light and fluffy (about 3-4 minutes).
Step 3: Gradually add the granulated sugar to the butter mixture, beating until well combined and fluffy, scraping down the sides of the bowl as needed.
Step 4: Add the eggs one at a time, beating well after each addition until fully incorporated. Stir in the vanilla extract.
Step 5: In a separate bowl, whisk together the all-purpose flour, baking powder, and salt.
Step 6: Gradually add the dry ingredients to the wet ingredients in three additions, alternating with the milk. Begin and end with the dry ingredients. Mix on low speed just until combined, being careful not to overmix.
Step 7: Pour the batter evenly into the prepared Bundt or tube pan.
Step 8: Bake for 70-80 minutes, or until a wooden skewer inserted into the center of the cake comes out clean. The top should be golden brown and spring back when lightly touched.
Step 9: Let the cake cool in the pan on a wire rack for 15-20 minutes before inverting it onto the rack to cool completely. Do not glaze until the cake is completely cool.
Step 10: Prepare the Cream Cheese Glaze: In a medium bowl, beat the softened cream cheese and butter until smooth. Gradually add the sifted powdered sugar, beating until creamy. Stir in the vanilla extract. Add milk or heavy cream, 1 tablespoon at a time, until the glaze reaches your desired drizzling consistency.
Step 11: Prepare the Homemade Caramel Drizzle: In a heavy-bottomed saucepan, combine the granulated sugar and water. Cook over medium heat, stirring until the sugar dissolves. Once dissolved, stop stirring and bring to a boil. Cook without stirring, swirling the pan occasionally, until the sugar syrup turns a rich amber color (this can take 8-10 minutes).
Step 12: Carefully and slowly pour the warmed heavy cream into the hot caramel (it will bubble up vigorously). Stir gently until smooth. Remove from heat and stir in the butter and sea salt (if using) until melted and combined. Let the caramel cool slightly to thicken before drizzling.
Step 13: Once the cake is completely cool, drizzle generously with the cream cheese glaze, allowing it to drip down the sides. Then, drizzle with the homemade caramel sauce. Slice and serve!