Preheat the oven to 400F. Line a baking sheet with parchment paper. Place the peppers on the baking sheet and drizzle lightly with a bit of olive oil and sprinkle with some salt. Rub around to coat. Arrange them cut-side-down and bake for 10 minutes while you make the filling.
In a high-speed blender (or food processor), add the carrots and celery and blend/pulse until finely chopped. Scrape down the sides and under the blade, then add the onion and garlic and blend again until everything is chopped up.
In a large skillet over medium heat, warm the olive oil. Add the onion mixture and ½ teaspoon salt. Cook for 7-10 minutes, stirring occasionally, or until the water has evaporated and things are looking very soft and caramelized.
Push the onion mixture to the sides and place the beef in the center of the skillet. Break up into chunks and sprinkle with the remaining ½ teaspoon salt. Cook, continuing to break into smaller chunks, until almost cooked through, about 2-3 minutes. Mix it all up with the onion mixture and continue to cook until the meat is cooked through, about 1 more minute.
Stir in the greens until wilted down (or thawed if using frozen), then pour in the wine or broth. Let it simmer, stirring occasionally, until most of the liquid has evaporated, about 2-3 minutes.
Turn off the heat and stir in the parmesan. Flip the peppers over so the cut side is facing up. Scoop the meat mixture into each pepper. Top with a spoonful of marinara followed by a sprinkle of cheese.
Transfer back to the oven and bake for 10-15 minutes or until the cheese is melted and meat mixture is browned/crispy on top.