1. Heat a grill to medium (350° to 450°). Cut 18 thin diagonal slices from baguette, angling knife so each slice is 3 to 4 in. long. Save remaining bread for another use. Set baguette slices on a tray and brush all over with about 1 tbsp. oil.
2. Arrange bread on cooking grate and grill with lid down, turning once with tongs, until browned, 1 to 3 minutes total. Transfer to a platter.
3. Heat a large cast-iron skillet or other oven-proof frying pan on cooking grate, with lid down, until water dances when sprinkled on skillet, 8 to 10 minutes. Add 1 1/2 tbsp. oil and spread with a heatproof brush. Pour tomato halves into pan, then quickly turn with tongs so all are cut side down. Sprinkle with 1/4 tsp. each salt and pepper. Cook with grill lid down, without stirring, until juices evaporate and tomatoes are blackened on cut side, 10 to 15 minutes. Gently loosen tomatoes from pan with a wide metal spatula as they’re done and transfer to a bowl.
4. Spoon ricotta into a bowl and drizzle remaining 1/2 tbsp. oil on top. Put basil in another bowl. Set out toasts with tomatoes, ricotta, basil, salt, and pepper so people can build and season their own bruschettas.