Place the whole bell peppers on a grill tray and put them under the grill (broiler). Alternatively, use heat-proof tongs to carefully hold the peppers over a gas hob flame.
Grill the peppers until they’re blackened and charred on all sides, turning them occasionally for even cooking. This should take about 12 minutes. Once done, wrap the peppers in foil and let them cool slightly; the steam will help make the skin easier to peel off.
While the peppers are grilling, cook the pasta and prepare the arrabbiata sauce. Bring a large pot of water to a boil and cook the penne according to the package instructions.
In a large skillet, heat the oil and add the onion. Cook over medium heat, stirring occasionally, for 2-3 minutes until the onions begin to soften. Add the chorizo and cook for another 3-4 minutes, until it releases its oils and starts to darken.
Stir in the garlic and tomato paste, cooking for 1 minute. Then add the canned tomatoes, thyme, dried chili flakes, and sugar. Bring the mixture to a gentle simmer and let it cook for 10 minutes.
By this time, the foil-wrapped peppers should have cooled slightly. Place them on a cutting board, remove and discard the charred skin, then slice the peppers, discarding the seeds. Add the chopped peppers to the arrabbiata sauce.
Once the pasta is cooked and drained, add it to the arrabbiata sauce. Use a spoon and tongs to stir everything together until the pasta is fully coated in the sauce. Stir in the mozzarella chunks and heat for another minute before turning off the heat.
Top the arrabbiata with a sprinkle of Parmesan, freshly ground black pepper, chili flakes, and chopped spring onions (scallions). Serve it directly from the pan.