Season the ground beef with ½ tsp. kosher salt and ¼ tsp. ground black pepper. Form the mixture into 4 patties (each will be ¼ lb.), and set aside.
Heat ½ tbsp. olive oil in a fry pan over medium-high heat.
Once hot, add the sliced mushrooms and onions and sauté until caramelized and golden-brown, about 8-10 minutes.
Heat another large skillet or griddle over high heat and add the remaining ½ tbsp. olive oil.
Once hot, add the patties and sear until golden brown on each side, about 1-2 minutes per side. Then, turn the heat to medium-high and cook for an additional 3-4 minutes per side. Then, remove from heat,
To assemble the burger, spread 1-2 tbsp. pesto on the inside of the buns. Then, on the bottom bun, place the patty, followed by about 1 tbsp. goat cheese, and then the sautéed onions and mushrooms. The heat from the mushrooms and onions will help to melt the goat cheese some. Place the top bun on top and serve.