Line a cutting board with 2 sheets of paper towel. Top with tofu and 2 more sheets of towel. Top with another cutting board or flat object and place a heavy object on top. Press for at least 10 minutes to extract liquid from tofu. Using your hands, crumble tofu into 1/2 inch chunks.

In large bowl, whisk together 2 Tbsp oil, 2 Tbsp water, tomato paste, soy sauce, chipotle pepper, paprika, and cumin. Remove 1/4 cup sauce; set aside. Add crumbled tofu to sauce in bowl and toss well to coat.

Heat large, heavy-duty skillet over medium-high. Add tofu and heat until warmed through, stirring a couple of times. Pour reserved sauce over hot tofu and mix well.

Remove tofu from skillet and set aside. Add remaining 2 tsp oil to skillet. Heat shallots for 2 minutes. Add mushrooms and thyme to skillet and heat until mushrooms have softened.

Stuff corn tortillas with tofu and mushrooms.