Add 1/4 cup tomato paste. Cook, stirring often, until the tomato paste breaks up and stains the oil, darkens in color, and starts to stick to the bottom of the skillet, about 3 minutes. Add 2 tablespoons Calabrian chili paste, the lemon zest, and 3/4 teaspoon kosher salt. Stir and cook for 30 seconds more. Remove the skillet from the heat.