Melt 1/2 cup butter in a large frying pan over medium-low heat; cook and stir lobster into melted butter until heated through, about 5 minutes. Season with salt and pepper.
Whisk cornstarch and about 1 tablespoon cream together in a small bowl until smooth. Pour remaining cream into lobster, stir in cornstarch mixture; cook and stir until cream sauce comes to a simmer and thickens slightly, about 5 minutes.
Toast bread and spread with about 2 tablespoons butter. For each serving, pour some creamed lobster over one buttered piece of toast, top with another piece of toast, and pour more creamed lobster over the top.