Spread the tofu over a paper towel-lined baking sheet and let it drain for 20 minutes, then gently press dry with additional towels. Season the tofu with salt and pepper. Heat a portion of the oil in a 12-inch nonstick skillet over high heat until just smoking. Add the tofu and cook, turning occasionally, until browned on all sides, 8 to 10 minutes, then transfer to a bowl.

Add the remaining oil to the now-empty skillet and heat over medium-high heat until shimmering. Add the mushrooms and cook until browned, about 4 minutes. Stir in the chili-garlic sauce, garlic, and ginger and cook until fragrant. Pour in the broth.

Break the ramen into chunks and add to the skillet. Bring to a simmer and cook for 2 minutes, tossing the noodles constantly with tongs to separate them, until they are just tender but liquid still remains in the pan.

Stir in the vinegar, soy sauce, and sugar. Add the spinach one handful at a time, stirring until wilted and the sauce has thickened. Return the tofu to the skillet and heat through, about 30 seconds. Serve hot.