Preheat oven to 350 degrees F (175 degrees C). Butter a casserole dish.
Whisk milk, sugar, and flour together in a large bowl. Add eggs, vanilla extract, thyme leaves, black pepper, and salt; whisk until batter is smooth.
Spread blackberries and peach slices out in the prepared casserole dish. Pour batter over the top.
Bake in the preheated oven until fruit is hot and batter is set, about 45 minutes. Cool completely.