Preheat oven to 400 degrees. Break off 2 cloves garlic; finely chop and reserve. Trim tip off each garlic head, exposing tops of cloves. Place heads on foil, drizzle with 1 teaspoon olive oil, and season with 1/4 teaspoon salt and 1 teaspoon thyme. Wrap tightly in foil. Roast until garlic is soft, about 45 minutes. Squeeze cooked garlic from cloves and discard skins.
Mix chopped garlic with lemon zest, parsley, and a pinch of salt and pepper; set aside. Place the shiitakes on a baking sheet and toss with 2 tablespoons olive oil, 1/4 teaspoon salt, and remaining thyme; roast until sizzling and tender, about 12 minutes. Sprinkle with garlic, parsley, and lemon mixture.
Heat a grill pan over medium-high heat and toast bread on both sides until golden brown. Spread roasted garlic on one side of each piece of toast and top with 3 mushroom caps. Serve warm.