Cook potatoes in boiling salted water to cover until just tender.
Drain potatoes and transfer to a bowl.
Melt butter with 1/4 teaspoon salt and 1/4 teaspoon pepper in a large nonstick skillet over medium heat; add onions and cook, stirring occasionally, until pale golden, about 5 minutes.
Add to potatoes and mash gently, leaving larger lumps.
Add 2 tablespoons oil to skillet and heat over medium heat.
Add potato mixture and pat out evenly.
Cook, partially covered, without stirring, until underside is golden brown, about 10 minutes.
Keep warm, covered, off heat.