Chiles:

• Preheat oven to 375 degrees F. Place 2 large poblano chiles on a baking sheet and drizzle with 2 tablespoons olive oil, salt, and pepper. Roast in oven until skin is blackened, about 15 minutes.
• Remove chiles from oven and place in a bowl, then cover tightly with plastic wrap. Let chiles rest in bowl for 15 minutes. Remove chiles from bowl and peel and seed the chiles, then coarsely chop.

Queso Sauce:

• Optional: saute diced onion and jalapeno in oil or butter in a skillet until tender. Wipe out the skillet and continue.
• Melt 1 tablespoon unsalted butter in a large skillet over medium heat and then whisk in 1 tablespoon all-purpose flour and cook for one minute.
• Add 1 1/2 cups whole milk, increasing heat to medium-high, and whisk constantly until sauce thickens, about 5 minutes. Turn heat to low and stir in 8 ounces pepper jack cheese, grated, 1 medium red onion, finely chopped, and 1-2 jalapeno peppers, seeded and finely diced.
• Season with salt and pepper and cook on low for about 5 minutes, stirring frequently, then remove from heat and keep warm.

Fry the tomatoes now. Please see separate post on Fried Green Tomatoes.

Burgers:

• Divide 1 1/2 pounds ground chuck into 4 equal portions about 3/4 inch thick.
• Make a depression in the center of each burger and season each side with salt and pepper.
• Cook the burgers either on the grill or in a skillet.

Assembly:

• Place burger on bottom half of toasted bun and top with a few pieces of the chopped poblano chile, 1 fried green tomato slice, a couple of tablespoons of the queso sauce, crumbled tortilla chips, and arugula.
• Cover with top half of bun and serve immediately.