Put the potatoes in a large pot and cover with cold water by 2 inches. Add 2 tablespoons salt and bring to a boil. Cook until a skewer
inserted into the center of each potato meets with no resistance, about 20 minutes. Drain
well and let them cool slightly while you prepare the mushrooms.
Heat 2 tablespoons each of the butter and canola oil
in a large cast-iron pan over high heat until the mixture begins to shimmer. Add the mushrooms, garlic and shallots
. Cook until the mushrooms are golden brown and all of the liquid has evaporated, and the shallots are tender. Transfer to a bowl.
Cut the potatoes into 1/2-inch dice
, keeping the skin on. Heat the remaining 2 tablespoons butter and oil in the same pan over medium-high heat, and heat until the mixture begins to shimmer. Add the potatoes and season with salt and pepper. Spread in one layer and cook, pressing with a spatula
, until crisp
and deep golden brown on the bottom, about 5 minutes. Stir in the mushrooms, parsley, thyme
and vinegar. Toss to warm through, 1 to 2 minutes. Season with salt and pepper. Transfer to a platter and drizzle
with olive oil. Serve hot or at room temperature.