Heat the oil and melt the butter in a medium heavy stockpot over medium-high heat. Add the onions, celery, and carrots and cook until soft, about 4 minutes. Add the shallots and garlic and cook until softened, about 2 minutes. Stir in the flour and continue to stir until the mixture is a light blond color, about 2 minutes. Add the brandy and stir for 30 seconds, scraping the bottom of the pot with a wooden spoon to release browned bits.
Add the lobster shells, then stir in the shrimp stock. Bring to a boil over high heat. Reduce the heat to medium-low. Add the tomato paste, salt, paprika, and cayenne. Simmer uncovered, stirring often, until the sauce is lightly thickened, about 1 hour.
Strain the sauce through a fine-mesh strainer into a medium saucepan. Add the cream and bring to a boil over medium-high heat. Reduce the heat to medium and simmer briskly until reduced to about 3 cups, about 15 minutes. Use warm. (The sauce can be stored in an airtight container in the refrigerator for up to two days.)
Yield: about 3 cups