For the burgers: Heat the coconut oil in a large nonstick skillet set over medium heat. Cook the onions and garlic, stirring occasionally, until translucent, 3 to 4 minutes. Transfer to a large bowl and cool for 5 minutes.
Add the bison, tomato paste, cumin, salt, black pepper and cayenne pepper to the onion mixture, and stir to combine. Form into four 1-inch-thick burgers. Place the skillet back over high heat, add the burgers and cook until an instant read thermometer registers 160 degrees F, 5 to 6 minutes per side. Remove from the pan and rest the burgers for 3 to 5 minutes.
For the aioli: In a small bowl whisk together the mustard, tomato paste, yolk and garlic. While whisking continually, slowly drizzle in the canola and olive oils, until all the oil is incorporated and the mixture is thick and glossy. Whisk in the lemon juice and season with cayenne pepper and salt.
Place each patty in a lettuce leaf, then top with tomato slices, shaved red onion and 2 teaspoons of the spicy aioli; wrap the burgers in the lettuce and serve with kale chips.
If you have concerns about salmonella, replace the egg yolk and oils with canola mayonnaise.
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