Make the relish: peel the lemons with a peeler and then finely dice the zest. Cut the lemons in half and juice them. In a bowl, combine the lemon zest, red onions, cherries, capers, walnuts, jam, basil, dill, and red pepper flakes. Mix well then add the lemon juice, pomegranate molasses, and liquid smoke. Set aside to come together for at least 30 minutes.

Make the cherry–mustard sauce: combine the cherries, pomegranate juice, lemon juice, brown sugar, and cinnamon in a pot and bring to boil. Lower the heat to a simmer and cook for about 15 minutes. Let cool, then transfer to a blender or food processor. Add the mustard and blend until well combined. Reserve until ready to use. (This should keep if in the refrigerator for 2 weeks.)

Make the patties: heat the oil in a large sauté pan over medium heat. Add the mushrooms and cook until tender, about 10 minutes. Transfer the mushrooms to a food processor and blend until smooth. In a large bowl, mix together the puréed mushrooms with the rest of the ingredients. Form into 4 patties and set aside until ready to cook.

Grill the burgers: heat a lightly greased large cast-iron skillet over high heat until it’s about to smoke. Cook the burgers on one side for about 4 minutes, or until seared well. Reduce the temperature to medium and flip the burgers to sear on the other side for another 4 minutes, or until the internal temperature of the patties registers 155°F on a meat thermometer. Top each patty with a slice of Brie and cover until the cheese has melted, about 1 minute.

Meanwhile, toast the buns. Combine the apricot jam and liquid smoke in a small bowl. Brush the jam on cut side of the top buns before toasting them in a 350°F oven for 10 minutes. Remove from the oven and top with a basil leaf.

To serve, place 4 basil leaves on each bottom bun and top with the relish. Place the patty on top and finish with the cherry mustard and top bun.