For caramelized onions, melt butter with olive oil in a large skillet over medium-low heat. Add onions, beef broth, salt, and pepper. Cook until onions are a deep golden brown, stirring occasionally, 20 to 25 minutes. Remove from heat and set aside.

Bring potatoes to a boil in a pot with enough cold, salted water to cover by an inch; cook until fork tender, about 20 minutes. Drain; return potatoes to the pot, dry potatoes in the pot over medium-high heat for about 30 seconds.