Author Leah Eskin finds bean-based burger substitutes to be tired. While experimenting, she realized that the additions were really satisfactory in their own right, and, thus, came up with this recipe.
Heat olive oil in a wide, heavy skillet. Add the onions, 1/8 tsp salt and a few grinds of pepper. Cook, stirring often, over medium-heigh heat, until onions are browned and sticky/crispy, about 15 minutes. Remove pan from heat.
Meanwhile, in a second wide, heavy skillet, melt butter. Add all the mushrooms, garlic, 1/8 tsp salt and a few grinds pepper. Cook over medium-high heat, stirring frequently, until mushrooms are richly browned, about 15 minutes.
Increase heat to high, pour in cognac and cook until liquid disappears, 1 minutes. Remove pan from heat.
Split buns; lay them open-faced on a broiler rack. Cover both halves with cheese. Slide under the broiler just until cheese has melted, 1 to 2 minutes. Set buns on serving platter.
Heap mushrooms onto each bottom bun. Top with onions. Cover with top bun. Enjoy.