Put the oil in a large pot over medium heat. Add the onion and ginger and cook, stirring frequently, until the vegetables soften and begin to turn golden, 5 to 10 minutes. Put the silken tofu in a small bowl and whisk until smooth. (It will go through an awkward “broken” stage — just keep whisking until the mixture emulsifies.)
Add the curry powder, salt, and pepper to the onion mixture and cook, stirring constantly, until fragrant, about a minute. Start adding the spinach a handful at a time, until the pan is full. Stir frequently and adjust the heat as necessary so the spinach softens but doesn’t burn; when there’s room in the skillet, add more spinach and stir, repeating until all the spinach is used. Then cook, stirring occasionally, until the pan is almost dry, just another 1 or 2 minutes.
Add the silken tofu and cook, stirring constantly and adjusting the heat as necessary, until the mixture bubbles gently but steadily. add the firm tofu and cover. Cook, stirring once or twice, until the cubes are heated through, 2 to 3 minutes. taste and adjust the seasoning and serve with the lemon wedges.