Preheat the oven to 350°F.
In a medium bowl, combine the chopped mushrooms and onion. Drizzle with 2 tablespoons olive oil; toss to coat. Spread the mixture onto a parchment-lined, rimmed baking sheet. Season with salt and pepper. Bake for 1 hour, until dark brown and mostly dry. Set aside to cool.
Use a food processor to chop the almonds to a coarse meal texture. Transfer chopped almonds to a large bowl and set aside. Add the tofu, remaining 1/4 cup oil, tahini, tamari, lemon juice, garlic, and thyme. Puree until the consistency is smooth.
Transfer the tofu mixture to the bowl with the almonds; stir to combine.
Add the mushroom mixture and stir again to distribute throughout.
Adjust seasoning to taste then cover and refrigerate until chilled, at least 2 hours and up to overnight. This is one of those recipes that tastes best the next day!