For the ketchup: Saute the shallots and garlic in the olive oil in a large skillet over low heat until translucent, 4 to 6 minutes. Add the honey and cook for 2 to 3 minutes more. Add the tomatoes, corn syrup, vinegar, sugar and chipotle puree and simmer for 30 minutes. Puree the mixture in a blender or food processor, adding vegetable stock if the ketchup is too thick. Season with salt and pepper.
For the mustard aioli: Combine the lemon juice and egg yolk in a food processor. Whisk together the canola and olive oil, and then slowly stream in until the mixture is thick and emulsified. Alternatively, this can be done in a mixing bowl with a whisk. Add the mustard, mustard powder and salt and combine. Season with more salt if needed.
For the burger: Preheat the oven to 375 degrees F. Heat the grill to high heat. Brush both sides of the bacon with some of the smoked chili ketchup. Place on a baking sheet and bake for 15 to 20 minutes, turning halfway through.
Gently fold the butter into the ground meat along with the paprika and cumin. Form the beef mixture into 6 patties, and sprinkle both sides liberally with salt and black pepper.
Brush the brioche buns on each side with olive oil and grill the insides until golden brown, 1 to 2 minutes. Grill the burgers until medium rare, 3 to 4 minutes per side. Once you flip the burger, add a thick slice of the cheese to each and keep the cover closed to let melt.
Spread the mustard aioli on one side of the buns and the smoked chili ketchup on the other. Place the burgers on the bun cheese-side up and top each with 2 strips of bacon.