Preheat broiler to high heat. Line a baking sheet with foil.
Wash and thoroughly dry red bell pepper and Hatch chiles. Place red bell pepper and whole green chiles on foil lined baking sheet and place in oven 4 to 6 inches below the heating element. Roast peppers and chiles for 10-12 minutes or until the skin is charred and blistered. Using tongs, flip hatch chiles over, halfway through cooking, and roast opposite side. Remove roasted peppers and chiles from oven and place in a heat-safe bowl. Cover bowl tightly with plastic wrap and set aside for 10-15 minutes. Once chiles have cooled, cut off tops and scoop out seeds. Peel away outer charred skin of both peppers and chiles and dice into small pieces.
Meanwhile, cut corn from cob (or use ½ cup thawed frozen corn) and place on foil lined baking sheet and place under broiler. Roast corn for 6-7 minutes or until golden brown. Let corn cool completely.
In a large bowl, stir together the chopped roasted red bell peppers and green chiles, corn, mayonnaise, lime juice, mustard, 1 ½ teaspoons Stubb's Pork Spice Rub, green onion, cilantro, ¼ cup cornmeal, and ¼ teaspoon each salt and black pepper. Carefully fold in crab meat, being careful not to over mix.
In a small bowl, stir together remaining cornmeal, Stubb's Pork Spice Rub, salt and black pepper. To form crab cakes, use about 2 tablespoons of the crab mixture and shape into into a patty about 1 1/2 inches thick. Dip prepared crab cake into cornmeal mixture and place on a clean foil lined baking sheet. Repeat with remaining crab mixture until 12 individual crab cakes are formed. Cover and refrigerate for at least 20 minutes to 1 hour.
Heat oil in a large skillet over medium-high heat. Carefully place 4 crab cakes in hot skillet and cook until golden brown, about 4 to 5 minutes. Carefully flip crab cakes and cook on opposite side until golden brown, an additional 3 to 4 minutes. Transfer cooked crab cakes to a paper towel lined plate. Repeat cooking process with remaining crab cakes.
Serve crab cakes immediately with prepared Green Chile Aioli.
Green Chile Aioli: In a small bowl whisk together mayonnaise, Stubb's Green Chile Marinade, lime juice and zest. Season to taste with salt and black pepper. Serve immediately with Southwestern Crab Cakes or cover and refrigerate.