Heat oven to 400° F. Microwave 4 tablespoons of the butter in a large microwave-safe bowl until melted. Divide the dough into 12 pieces, roll into balls, and toss in the butter to coat; reserve the bowl. Place the balls in the cups of a 12-cup muffin tin and, using kitchen shears, snip an X in the top of each; season with 1 teaspoon salt. Bake until golden brown, 18 to 22 minutes. Brush the hot rolls with any melted butter left in the bowl.
Meanwhile, melt the remaining 2 tablespoons of butter in a large saucepan over medium heat. Add the celery, onion, potato, ¾ teaspoon salt, and ½ teaspoon pepper and cook, stirring occasionally, until softened, 5 to 7 minutes.
Add the flour and thyme to the saucepan and stir to combine. Increase heat to medium-high and slowly mix in the milk and broth. Simmer, stirring frequently, until thickened, 4 to 5 minutes. Add the shrimp and peas and cook until the shrimp are opaque throughout, 2 to 3 minutes. Serve with the rolls.