Add the potatoes to a large pot, cover by 2 inches with water, season with salt and bring to a boil. Boil until the potatoes are just fork tender but firm, about 10 minutes. Drain and set aside to cool.
In the meantime, coat a large saute pan with canola oil and set over medium-high heat. Add the shiitakes, garlic paste and shallots. Season with salt and pepper and saute until the mushrooms are golden and tender, 7 to 10 minutes. Just before the mushrooms are ready, toss in the thyme and parsley. Remove the mixture from the heat and allow to cool.
Heat a grill to high.
Now, slice your cooled potatoes into 1/2-inch rounds. Drizzle them with a bit of canola oil and sprinkle with salt and pepper. Grill the potatoes until marked and cooked through, 2 to 3 minutes per side.
Toss the cooled mushroom mixture with the goat cheese. Add some red wine vinegar, extra-virgin olive oil and salt and pepper. Top each piece of grilled potato slice with a spoonful of the mushroom mixture. Garnish with chervil.