Preheat the oven to 400 degrees F. Place the chilies and red pepper on a baking sheet, toss with 2 teaspoons of the canola oil and roast for 20 minutes. Once cool enough to handle, finely chop.
Heat the remaining teaspoon of canola oil in a saute pan over medium heat, add the onion and garlic and sweat until softened, 5 to 8 minutes. Add the tomato paste and cook until lightened in color, 1 to 2 minutes.
Combine the pepper mixture with the vinegar, lime juice, salt, paprika, and red pepper flakes in a food processor and pulse until combined. While the food processor is running, stream in the olive oil slowly to achieve a smooth puree, similar in to texture to ketchup. Set aside 1/3 of the sauce for serving.
Place the steak and the remaining 2/3 of the sauce in a large re-sealable plastic bag; toss to coat and marinate in the refrigerator for 2 to 4 hours.
Preheat a grill to medium-high heat. Remove the steak from the marinade, pat dry with paper towels, and season with salt and pepper. Grill the steak for 4 to 5 minutes per side for medium-rare. Let the steak rest for 10 minutes before slicing thinly against the grain. Serve with the reserved sauce on the side.
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