8 soft slider buns (potato are especially nice)
Heat olive oil in a wide, heavy skillet. Add onions, 1/8 teaspoon salt and a few grinds of pepper. Cook, stirring often, over medium-high heat until onions are browned and sticky/crispy, about 15 minutes. Pull pan off heat.
Meanwhile, in a second wide, heavy skillet, melt butter. Add both kinds of mushrooms, garlic, 1/8 teaspoon salt and a few grinds of 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 minute. Pull pan off 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, 1-2 minutes. Set buns on a serving platter.
Heap mushrooms onto each bottom bun. Top with onions. Cover. Chomp.
Leah Eskin is a Tribune Newspapers special contributor. Email her at email@example.com.