Preheat grill to 400℉.
Parboil the potatoes wedges in boiling water for about 3-5 minutes until just beginning to get fork-tender. (It is very important that you not overcook the wedges, watch them very closely.). Remove from the boiling water and place in an ice bath to stop the cooking. Drain and place on paper towels to dry.
Dry the potato wedges completely. Toss them gently with the olive oil and the cajun seasoning. Spread onto a grill pan leaving space between each to circulate air around each wedge.
Grill for 12-18 minutes, turning every 4 minutes, being careful not to burn the wedges. (The wedges will get crispy on the outside and will be tender on the inside.)
Once done, remove and place on a platter with the spicy garlic ketchup and the chipotle red pepper aioli.
Combine the ketchup, hot sauce, and roasted garlic. Stir well to combine and store in the refrigerator until ready to serve.
Combine the red peppers, onion, garlic, vinegar, honey, mustard, and chipotles in adobo in a blender. Season with salt and pepper and blend until smooth. With the motor running, slowly add the olive oil and blend until emulsified. Strain the sauce into a bowl.
Add the mayonnaise and stir until well combined. Store in the refrigerator until ready to serve.