Pre-heat broiler. Coat Squash in oil, season with salt and pepper. Place cut side up on baking sheet and roast on the bottom shelf (45 minutes) until the squash starts to brown.
On a sheet tray broil peppers on the highest oven rack until they blister (five minutes). Flip and broil 3 minutes more. Remove stems and seeds. Emulsify peppers in blender with lemon juice, sea salt, pepper, and red wine vinegar. Stir in onions.
Lower oven to 375. In a skillet melt butter and saute Brussels Sprouts until caramelized and soft over a medium heat.
Remove cooked squash from the oven and scoop out flesh with a fork, save skins for serving.
Combine sprouts, squash, and cheese and fill the squash skins. Top with sauce and more grated cheese. Reheat on an oven safe platter at 250 degrees until cheese melts.