In a large pot of boiling, salted water, cook the corn until the kernels are crisp-tender, about 5 minutes. Remove from the pot using tongs.
Using a small food processor, puree 8 oil-packed sun-dried tomatoes with 1 tbsp. of their oil and 3 tbsp. goat cheese. In a nonstick skillet, toast 1-1/2 cups fresh breadcrumbs in 2 tbsp. butter. Spread some tomato mixture on each ear of husked corn. Lightly coat with breadcrumbs and place on a rack-lined baking sheet; bake at 375 degrees until tender, about 10 minutes.