Clean the oyster mushrooms and trim off any tough ends. Using your hands or two forks, pull the mushrooms apart into long, shredded pieces to create a pulled-pork texture.
Heat the olive oil in a large skillet over medium heat. Add the sliced onion and cook for 3–4 minutes until softened. Add the garlic and cook for another 30 seconds.
Add the tomato paste, smoked paprika, chili powder, garlic powder, onion powder, salt, and black pepper. Stir and cook for about 1 minute until the tomato paste darkens slightly and the spices become fragrant.
Add the shredded mushrooms and toss well to coat them in the seasoning mixture. Cook for 5–7 minutes, stirring occasionally, until the mushrooms begin to soften and release some of their moisture.
Pour in the vegetable broth and BBQ sauce. Stir until everything is evenly coated. Reduce the heat to medium-low and simmer for 10–15 minutes, stirring occasionally, until the sauce thickens and clings to the mushrooms.
For an even more pulled-pork-inspired texture, turn the heat back up to medium-high for the final 2–3 minutes. Let some of the mushrooms caramelize and develop crispy edges while remaining saucy.
Spread the vegan butter on the cut sides of the brioche buns. Toast them cut-side down in a skillet over medium heat until golden brown.
Pile the BBQ pulled mushrooms onto the toasted brioche buns.
