Slice tops off peppers and place peppers on a microwave-safe plate. Remove stems from pepper tops and discard. Dice flesh from pepper tops and set aside 1/2 of the diced peppers; save remaining diced peppers for another use.
Microwave peppers on high for 3 minutes until partially cooked.
Place frozen riced cauliflower in a microwave-safe bowl and microwave on high for 4 minutes, stirring halfway through.
Heat olive oil in a large nonstick skillet over medium-high heat until hot, about 1 minute. Add beef, mushrooms, carrots, celery, onion, and reserved diced peppers and cook until onions begin to turn translucent and beef is nearly cooked, about 5 minutes. Stir in Italian seasoning, red pepper flakes, oregano, salt, and pepper; cook for 1 minute. Add cooked riced cauliflower and garlic; stir and cook until beef is browned and crumbly, breaking up any chunks with a spoon, 2 to 3 more minutes.
Preheat the oven to 350 degrees F (175 degrees C).
Add drained tomatoes, tomato paste, and fresh basil to the skillet and cook until nearly all liquid is absorbed, about 5 more minutes. Turn off heat and allow beef mixture to cool slightly, about 5 minutes.
Stuff beef mixture evenly into peppers. Stand peppers upright in a baking dish.
Bake in the preheated oven until peppers are tender and filling is hot, about 30 minutes.