Preheat oven to 375°F. Place bell peppers, skin side down, in a shallow baking dish and top with anchovies and garlic. Tear 1/4 cup basil leaves over top, season with kosher salt and black pepper, and drizzle with 2 Tbsp. oil. Bake until peppers are tender but still hold their shape and are slightly charred around edges, 35–45 minutes. Let cool.
Meanwhile, blend remaining 3/4 cup basil and remaining 1/3 cup oil in a blender until smooth; season basil oil with kosher salt and black pepper.
Arrange bell peppers on a platter. Top with tomatoes, ricotta, olives, and more basil, then drizzle with basil oil and season with sea salt and black pepper.