Smoky Chicken and Corn with Honey Butter

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1 stick unsalted butter, at room temperature

2 tablespoons honey

Kosher salt and freshly ground pepper

2 ears of corn, shucked and cut into 1-inch pieces

8 ounces shiitake mushrooms, stemmed and thinly sliced

1 bunch scallions, trimmed and cut into 2-inch sections

4 sprigs fresh thyme

4 skinless, boneless chicken breasts (6 to 8 ounces each)

1/2 teaspoon sweet smoked paprika