In an 8- to 10-inch frying pan over high heat, stir onion in 1 1/2 tablespoons olive oil often until lightly browned, 5 to 6 minutes. Add rice and pine nuts and stir until some of the rice is opaque and nuts are slightly browned, 2 to 3 minutes. Add broth, bay leaf, and thyme; stir, then cover. When boiling, turn heat to low and simmer, stirring occasionally, until rice is tender to bite, about 15 minutes; add 2 to 4 more tablespoons broth if liquid is absorbed before rice is tender. Remove from heat. Add salt to taste.
Lay half the pepper halves side by side, cut side up, in a shallow 8- by 12-inch casserole or pan. Mound rice filling equally in peppers, using it all. Lay remaining pepper halves, cut side down, on rice filling, matching sizes and shapes to bottom halves. Drizzle peppers with 1 1/2 to 2 tablespoons olive oil.
Bake in a 375º regular or convection oven until peppers are soft and slightly browned, about 30 minutes. With a wide spatula, transfer filled peppers to a platter or plates. Serve hot, warm, or at room temperature.