Cook potatoes in large saucepan of boiling salted water until just tender, about 12 minutes. Drain potatoes. Cool. (Can be made 1 day ahead. Cover; chill.)
Melt 2 Tbsp butter with oil in heavy large skillet over medium-high heat. Add potatoes; sauté until golden, turning occasionally and adding 1 Tbsp butter halfway through cooking, about 18 minutes.
Melt 1 Tbsp butter in medium skillet over medium-high heat. Add all mushrooms; sauté until golden, 6 minutes.
Add mushrooms and parsley to potatoes; toss to combine. Season with salt and pepper.
Make it substantial with an egg (or two) on top!