Any combination of dried mushrooms will work here. We used a prepackaged mix that contains shiitake, wood ear, and porcini. To save time, you can substitute 1 1/3 cups canned pumpkin for the cooked, mashed squash.
Combine the mushrooms and boiling water in a bowl; cover and let stand for 1 hour. Drain. Slice mushroom caps; discard stems. Combine mushrooms, Tomatillo Purée, and Dried-Chile Purée in a small nonstick skillet; bring to a boil over medium-high heat. Reduce heat; simmer 5 minutes or until thick. Keep warm.
Place chiles on a foil-lined baking sheet; broil for 10 minutes or until blackened, turning occasionally. Place in a zip-top plastic bag; seal. Let stand 15 minutes. Peel chiles; cut in half lengthwise. Discard seeds and membranes. Slice each chile into 6 strips, and set aside.
Preheat oven to 350°.
Place squash halves, cut sides down, on a baking sheet; bake at 350° for 45 minutes or until tender. Cool; discard seeds and scoop out squash pulp. Combine squash pulp, 2 tablespoons pine nuts, honey, and salt in a microwave-safe bowl.
Place tortillas directly on middle rack in oven. Bake at 350° for 7 minutes (tortillas should be slightly pliable).
Microwave squash mixture at high 30 seconds or until hot. Spread 1/4 cup squash mixture over each tortilla; top with 1/4 cup mushroom mixture. Arrange 2 chile strips over mushroom mixture; sprinkle with 1/2 teaspoon pine nuts.