Step 1: Preheat oven to 350°F (175°C). Grease and flour a 9x13 inch baking pan or two 8-inch round cake pans.
Step 2: In a medium bowl, whisk together flour, baking powder, baking soda, and salt. Set aside.
Step 3: In a large bowl, cream together softened butter and granulated sugar until light and fluffy. Beat in eggs one at a time, then stir in vanilla extract.
Step 4: In a separate small bowl, combine cooled strong brewed coffee and buttermilk.
Step 5: Gradually add the dry ingredients to the wet ingredients, alternating with the coffee-buttermilk mixture, beginning and ending with the dry ingredients. Mix until just combined, being careful not to overmix.
Step 6: Pour batter into the prepared baking pan(s) and spread evenly. Bake for 30-35 minutes for a 9x13 pan, or 25-30 minutes for 8-inch rounds, or until a wooden skewer inserted into the center comes out clean. Let cool completely on a wire rack.
Step 7: While the cake cools, prepare the caramel sauce. In a heavy-bottomed saucepan, combine 1 cup granulated sugar and water. Heat over medium-high heat, swirling occasionally (do not stir), until the sugar dissolves and the syrup turns a rich amber color. This can take 8-12 minutes.
Step 8: Carefully remove from heat. Slowly and carefully pour in the warm heavy cream, whisking constantly (be cautious as it will bubble vigorously). Stir in the cubed butter and sea salt until smooth. Return to low heat for 1-2 minutes, stirring, until thickened slightly. Remove from heat and stir in vanilla extract.
Step 9: Once the cake is completely cool, pour the warm, gooey caramel sauce over the top, letting it drip down the sides.
Step 10: Serve immediately, or allow the caramel to set slightly for a thicker texture. Enjoy!