For the salsa: Place the lime juice, cilantro, salt, tomatoes, jalapenos, onions and peppers in a food processor. Pulse to combine, then set aside.
For the stuffed peppers: Preheat the oven to 350 degree F. Start by cutting the peppers in half lengthwise, leaving the stems intact. Remove the seeds and ribs inside the peppers.
Heat a skillet to medium-high heat and add the olive oil and onions, cook for about 1 minute. Next add the ground beef and garlic and cook until the onions become translucent, about 8 minutes.
In a separate bowl mix 1 cup of the salsa, the rice, sour cream and green onions. Add the ground beef mixture and combine thoroughly. Stuff the mixture into the peppers. Sprinkle each pepper half with 2 tablespoons of the cheese.
Place the stuffed peppers in a casserole dish, cover with foil and bake for 30 minutes. Remove the foil and continue to cook until heated through, 15 minutes. Top with basil and enjoy.