Step 1

Roast the vegetables: Preheat the oven to 375 degrees F.

Step 2

In the bowl of a food processor, pulse the carrots, celery and onions into small pieces, 12 to 15 times. Stir in the canola oil and season with salt. Spread the vegetables in a thin layer on a baking sheet, place in the center of the oven and roast until caramelized and tender, 12 to 15 minutes. Remove the baking sheet from the oven and let cool.

Step 3

For the cheese sauce: In a medium pot, simmer the cream over medium heat. Whisk in the mustard, soy, hot sauce and garlic. Sprinkle in the cheeses so they don't clump as they melt. Whisk until the cheese is melted and the sauce is smooth. Keep warm.

Step 4

For the burgers: In a medium bowl, break up the meat and spread it up on the sides. Sprinkle liberally with salt and pepper. Divide the meat into 12 portions and roll each into a ball. Place the meatballs on a clean surface and gently flatten them into small 1/2-inch patties.

Step 5

Heat a griddle or 2 large heavy-bottomed or cast-iron skillets and add half the canola oil to each. When the oil begins to smoke lightly, add the patties in a single layer and cook over high heat, using a metal spatula to flatten and "smash" slightly, for 2 minutes. Flip them on their second side, adding additional oil as needed, and press down again to smash and brown them, 2 to 3 minutes more.

Step 6

Stir the chopped pickles, pickle juice and ketchup into the roasted vegetables. Place a patty on each roll bottom. Spoon some roasted vegetable mix on each. Top with a little cheese sauce. Repeat this layering two times more. Pour over the remaining cheese sauce and red onion slices and top with the roll tops.