Preheat the oven to 400 degrees F.
Slice each pepper in half lengthwise, keeping the stem intact. Remove the ribs and seeds and discard, hollowing out each of the peppers. Sprinkle with salt and black pepper and place in an 8- by 8-inch baking dish.
Whip the goat cheese and ricotta together until light and airy in a mixing bowl, using a hand mixer, about 2 minutes. Stir in the thyme, 1/2 teaspoon salt and 1/2 teaspoon black pepper. Taste and adjust the seasoning, if necessary. Fill each pepper halfway with 2 teaspoons of the cheese mixture and level off with a small offset spatula.
Place the breadcrumbs in a small bowl. Pour the butter over the breadcrumbs and toss to combine. Sprinkle each pepper with the buttered breadcrumbs. Bake until golden and bubbly, 15 to 20 minutes.