Spread softened butter on the insides of the hamburger buns, and place buns butter side down in a hot skillet over medium heat. Cook until bun is golden and toasted. Remove buns from the pan.

Place oil in a medium pan, and heat over medium heat. Once hot, add sliced onions, and stir. Place lid on pan, and cook for 5 minutes to allow the liquid to be released from the onion. Remove lid, and add a pinch of salt. Cook, stirring regularly, adding a little bit of water if the onions start to burn, for 15-20 minutes, or until nicely golden and soft. Remove from heat, and set aside.

Place shredded cheese and cornstarch in a large bowl, and toss to combine.

Transfer coated cheese to a medium saucepan, and add evaporated milk.

Cook cheese and milk over low heat, stirring constantly until melted, bubbly, and thickened, about 5 minutes.

Mixture may look thin and grainy at first but will thicken and come together after heating. If desired, thin the cheese sauce with additional evaporated milk. There will be more cheese sauce than you need for a couple of burgers.

Preheat oven to 400° F. Line large baking sheet with parchment paper.

Using the small holes of a box grater, grate the Parmesan cheese.

With a tablespoon-measuring spoon, scoop 4 tablespoons of the grated Parmesan onto the prepared baking sheet. Leave at least ½-inch between each pile. Lightly press the mounds out until they are flat and approximately the size of the hamburger buns. Make as many crisps as burgers that you’re having.

Bake for 5-8 minutes. Remove from oven when edges just turn golden brown. Let cool completely on the baking sheet.

Place the bottom of the butter-toasted bun on the plate. Place the cooked patty on top of the bun. Spread the caramelized onions over the top of the patty. Drizzle the cheese sauce over the top of the onions. Add a handful of fresh arugula leaves to the top. Place the Parmesan cheese crisp on top of the arugula, and top with the butter-toasted bun.

Enjoy. Don’t forget the napkins!