Preheat Oven: Preheat your oven to 350°F (175°C) and grease and flour a 9×13-inch baking pan.
Mix Dry Ingredients: In a medium bowl, whisk together cake flour, baking soda, and salt.
Cream Butter & Sugar: In a large bowl, cream together the salted butter and granulated sugar until light and fluffy.
Add Eggs and Extracts: Beat in the eggs, one at a time, followed by rum, almond, and vanilla extracts.
Combine Wet Ingredients: In a separate bowl, whisk together the sour cream, milk, and butter-flavored shortening until smooth.
Alternate Adding Dry & Wet Ingredients: Gradually add the dry ingredients to the wet ingredients, alternating with the sour cream mixture, beginning and ending with the dry ingredients. Mix until just combined.
Bake the Cake: Pour the batter into the prepared pan and smooth the top. Bake for 30–35 minutes, or until a toothpick inserted into the center comes out clean. Let the cake cool completely.
Make the Salted Caramel Sauce: In a medium saucepan, heat the sugar over medium heat, stirring constantly, until it melts and turns amber. Add the butter, stirring until smooth, then slowly add the heavy cream and continue stirring until the sauce thickens. Stir in the sea salt to taste.
Assemble the Cake: Once the cake has cooled, drizzle the salted caramel sauce over the top. Slice and serve.