Heat a dry skillet or comal over medium heat. Toast the dried pasilla chiles, pressing with a spatula and turning until fragrant and pliable, 30–45 seconds per side; do not let them blacken.
Transfer chiles to a bowl and cover with 4 cups hot water. Weight them with a small plate to keep submerged and soak until softened, about 15 minutes. Drain, reserving 1/2 cup of the soaking liquid.
On the same hot skillet (or under a broiler on a sheet pan), char the tomatoes, onion, and garlic, turning occasionally until blistered and blackened in spots and the tomatoes have softened, 8–10 minutes. Peel the garlic if skins are loose.
In a blender, combine the softened chiles, charred tomatoes, onion, garlic, pulque, and 1/4 cup reserved chile soaking liquid. Blend until very smooth, adding a little more soaking liquid as needed to help it turn.
Heat the vegetable oil in a medium saucepan over medium heat. Carefully pour in the blended sauce and bring to a gentle simmer, stirring.
Simmer the sauce, stirring occasionally, until thickened enough to coat a spoon and the flavors have melded, 10–12 minutes. Season with kosher salt to taste and adjust consistency with a splash of soaking liquid if desired; simmer 1 minute more.
Let the salsa cool slightly. Serve warm or at room temperature, topped with crumbled queso añejo (for serving).