Croque Monsieur Burgers with Pistou on Brioche

Ingredients

For the patties:
16 ounces chuck, trimmed, cut into 1 1/2-inch cubes
16 ounces sirloin, trimmed, cut into 1 1/2-inch cubes
1 3/4 teaspoons kosher salt
For the Pistou:
2 large bunches fresh basil, leaves only, washed and dried
½ cup Colavita extra virgin olive oil
2 large cloves garlic, peeled and chopped
For the mornay sauce:
¼ cup butter
¼ cup all-purpose flour
2 cups milk
1 shallot, whole, peeled
½ teaspoon thyme (wrapped in a cheesecloth and tied)
1 teaspoon kosher salt
8 ounces gruyere cheese, grated
Vegetable oil, for brushing on the grill rack
12 thin slices Baked, or similar ham
6 soft brioche rolls, split
4 oz gruyere cheese, grated

Instructions

Prepare a medium-hot fire in a charcoal grill with a cover, or preheat a gas grill to medium heat. To make the patties: In separate batches, pulse 8 oz at a time of the chuck and sirloin in a food processor 10 times. Combine the chuck, sirloin, and kosher salt in a large bowl. Mix very gently to combine, being careful not to overmix the meat. Divide the meat into six equal portions, making a small indention in the middle to prevent the burgers from bulging. Set aside. To make the pistou: In a blender, combine basil, ¼ cup of olive oil, and garlic. Pulse to process. Add remaining ¼ cup oil in a thin stream to emulsify. Remove from the blender. To make the mornay sauce: Preheat a fireproof skillet on the grill to medium heat. Add the butter to the pan. When it has melted, add flour and stir well with a wooden spoon to mix. Cook the roux over medium-low heat for about 3 minutes. Remove the pan and let the mixture sit at room temperature for 15 minutes. Meanwhile, in a medium fireproof skillet, heat the milk until comes just below a boil. Return the roux to the grill, and whisk in hot milk to the pan. Add shallot and thyme. Simmer, whisking, for 15- 20 minutes, or until thick. Remove the thyme and shallot. Add salt and gruyere and stir until smooth. Brush the grill rack with oil and heat to medium-high heat. Grill the patties with the grill top closed for 4 minutes. Turn and grill until an instant-read thermometer inserted into the center of the patties registers about 155 degrees F, approximately 3 minutes longer. During the last few minutes of grilling, add 2 ham slices to the top of each patty to warm through. During the last 2 minutes of grilling the patties, place the rolls, cut side down, on the grill to toast. To assemble the burgers, place the patties to the bottoms of the rolls. Add a generous spoonful (2-3 Tablespoons) of mornay sauce to the top of the patties. Spread about 1 ½ Tablespoons of pistou on the top roll, and place on the patties. Return the patties to the grill with a piece of aluminum foil underneath the patties. Slather another 1 ½ Tablespoons of mornay sauce on top of each burger roll, and sprinkle with grated gruyere cheese. Close the lid and allow the gruyere to melt and bubble, about 1-2 minutes. If necessary, wrap a sleeve of aluminum foil around each patty to keep the sides from becoming too crispy. Remove from the grill and serve. Makes 6 burgers