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Preheat the oven to 400 degrees F (200 degrees C). Lightly grease a baking sheet.
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Bring water to a boil in a medium saucepan. Stir in rice. Reduce heat, cover, and simmer until liquid is absorbed, about 20 minutes. Remove from heat and set aside.
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Meanwhile, place peppers cut-side down on the prepared baking sheet. Roast in the preheated oven until tender and skin begins to brown, 25 to 30 minutes.
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While peppers are roasting, heat oil in a medium skillet over medium-high heat. Cook and stir onions, basil, Italian seasoning, salt, and pepper in oil for 2 to 3 minutes.
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Stir in tomato and cook for 5 minutes. Spoon in cooked rice and stir until heated through.
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Remove from heat, mix in feta cheese, and spoon mixture into pepper halves.
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Return peppers to the oven until warmed through, about 5 minutes.