Preheat oven to 350°F. Grease a 12-cup muffin pan with butter.
In a large bowl over a pot with ½-inch of simmering water, stir together chocolate and butter until completely melted, smooth and glossy; set aside to cool about 5-10 minutes.
Beat eggs with sugar in a large bowl for 2-3 minutes until pale, thick and fluffy. When you lift up the beaters, the egg mixture will form a slowly disappearing ribbon on the surface of the mixture when it falls back into the bowl. Beat in vanilla and salt then stir in warm chocolate mixture until evenly blended. Sprinkle in flour and stir until well incorporated and smooth. Divide batter evenly among greased muffin cups. Make a well in the center of each.
Stir together caramel and flour then spoon a teaspoon of the caramel into the well in the center of each brownie batter cup and swirl it in with a skewer. Bake for 15-17 minutes until set around the edges but still soft and in the middle. Transfer pan to a wire rack to cool completely before running a knife around the edges and inverting. Serve warm or cold!