Sandwich the tofu quarters between several layers of paper towels and weigh them down with a heavy plate for 20 minutes to remove excess moisture.

Combine the broth, rice, minced garlic, and salt in a small saucepan. Bring to a boil over high heat, then cover and reduce heat to low. Simmer until the liquid is fully absorbed and the rice is tender, about 15 to 20 minutes. Remove from heat and keep covered.

Pulse the drained tofu in a food processor until it is coarsely chopped into roughly 1/4-inch pieces, about 5 pulses. Transfer to a bowl and wipe the processor clean.

Pulse the tomatillos in the food processor until they are coarsely chopped, about 5 pulses.

Heat a portion of the vegetable oil in a large skillet over medium-high heat until it shimmers. Add the tofu and cook, stirring occasionally, until the pieces are golden brown and slightly crisp, about 8 to 10 minutes. Transfer the tofu back to its bowl.

Heat the remaining oil in the skillet and add the poblanos, onions, and jalapeño. Cook until the vegetables are softened and starting to brown, 8 to 10 minutes.

Stir in the remaining garlic, cumin, and oregano and cook until fragrant. Add the chopped tomatillos and simmer until the liquid has thickened and the tomatillos have softened into a sauce, about 10 minutes.

Return the browned tofu to the skillet and stir to combine. Season the filling with salt and pepper to taste.

Fluff the rice with a fork and stir in the cilantro. Warm the tortillas until pliable.

Spread the rice, cheese, and tofu filling across the center of each tortilla. Fold in the sides and roll tightly. Serve warm while the cheese is melted and the filling is hot.