Mix ricotta and 2 Tbsp. oil in a small bowl; season with salt and pepper.
Toss tomatoes, shallot, garlic, basil, parsley, and vinegar in a medium bowl; season with salt. Heat 4 Tbsp. oil in a skillet large enough to fit bread in a single layer over medium. Fry bread until deep golden brown on one side, about 4 minutes. Transfer to a cutting board, sprinkle fried side with salt, and cut into 1 ½" pieces. Toss into tomato mixture.
Spread ricotta mixture over plates and top with salad; drizzle with more oil.
