AKA “The Mullet” (spicy up front, sweet in the back)
Roast the jalapenos in a 400 degree oven for about 15 minutes on each side. Put them into a large bowl and cover with aluminum foil to sweat. Set aside.
Chop the onion and garlic. Cut the carrot width-wise into circles. Skin and cut the apple into small chunks.
Sautee the onion until transparent in olive oil, then add the garlic and carrot. Cook these until the carrot is starting to get soft, then add the apple and peppers. Add the vinegar and bring this mixture to a boil. Let it boil for about 10 minutes, then blend the mixture using an immersion blender or transferring to a food processor. Add salt, cayenne, and paprika to taste. Simmer this mixture for another 5-10 minutes, then remove from heat and let cool.
Refridgerate the resulting sauce; this recipe will keep in the fridge for several weeks.