To prepare the filling, coarsely crumble tofu onto two layers of a lint-free dish towel.

Wrap tofu in the towel and lightly press out excess moisture; set aside.

Heat oil in a large skillet over medium-high heat.

Add onions and cook until tender, about 4 minutes.

Add turkey and cook, stirring frequently, until just brown, about 8 minutes.

Add mushrooms, garlic, oregano, 1/4 teaspoon of the salt and pepper and cook, stirring occasionally, until the liquid has evaporated, about 10 minutes.

Add spinach in 2 batches and cook until just wilted, about 2 minutes each.

Stir in basil and tomato sauce, reduce heat to low, cover, and simmer for about 15 minutes.

Taste and adjust seasoning.

Meanwhile, whisk eggs and remaining 1/4 teaspoon salt together in a medium bowl.

Add flour and whisk until well blended and slightly thickened, about 1 minute.

Unwrap tofu, crumble it into small pieces and add it to egg mixture.

Stir well; set aside.

Meanwhile, cook lasagna noodles according to package directions in salted boiling water, but reduce the cooking time by 5 minutes.

The noodles should be slightly firm, as they will continue cooking in the oven.

Drain, rinse with cold water and drain again.

Preheat the oven to 350°F.

To assemble the lasagna, ladle 1/4 cup of the sauce into the bottom of a 9x13-inch baking dish and spread it out evenly.

Arrange 3 lasagna noodles on top of the sauce.

Place 1/3 of the tofu mixture on the lasagna sheets along with about a 1/4 of the sauce, distributing it evenly.

Repeat layering two more times with 3 lasagna noodles, 1/3 of the tofu mixture and 1/4 of the sauce.

Finish with a final layer of noodles and remaining sauce, taking care to spread the sauce evenly all the way to the corners.

Cover the dish tightly with aluminum foil and bake for 45 minutes.

Set aside, uncovered, to let stand for 15 minutes, then slice and serve.