Gather all ingredients.

Melt butter in a large skillet over medium heat. Add celery and shallots; cook and stir until shallots are tender, 3 to 5 minutes.

Heat half-and-half in a large pot over medium-high heat. Add celery and shallot mixture, and stir continuously until just about to boil.

Add oysters and their liquid, and season with cayenne pepper, salt, and pepper.

Cook, stirring continuously, until oysters curl at the ends. Turn off the heat and serve immediately.