Heat olive oil in a skillet over medium heat; cook and stir tomatoes, prosciutto, and shallots in hot oil until liquid cooks off, about 5 minutes. Add cream to shallot mixture; bring to a boil.
Stir vodka into cream mixture, return to a boil while stirring constantly, reduce heat to low, and season with salt and pepper. Cover the skillet with a lid and cook until flavors blend, about 3 minutes. Remove from heat and let stand until sauce thickens slightly, about 3 minutes more.