Place the dried porcini mushrooms in a heatproof bowl and cover with hot or boiling water; soak for 20–30 minutes.
Make the Easy 20 Minute Marinara or measure 3 cups of store-bought marinara and set aside.
Preheat the oven to 350°F (175°C).
Using a mandolin or sharp knife, slice each zucchini lengthwise about 1/8 inch thick. Lightly season the slices with kosher salt and let them sit 10 minutes to draw out moisture.
Blot zucchini slices dry with paper towels, arrange in a single layer on a lined baking sheet, and bake 10 minutes. Remove and set aside.
Heat the olive oil in a sauté pan over medium heat. Add a pinch of red pepper flakes and the garlic and cook until fragrant, about 30–60 seconds.
Add the diced onion (and any extra diced zucchini), season with salt, and sauté about 5 minutes until beginning to soften.
Add the crimini and shiitake mushrooms, dried oregano, dried thyme, and season with salt and pepper. Stir to combine.
Add the rehydrated porcini mushrooms (reserve the soaking liquid). Sauté the mixture about 15 minutes until most moisture has evaporated and the mushrooms begin to brown.
Pour in about 1/4 cup of the reserved porcini soaking liquid and continue cooking until the liquid evaporates and the mushroom mixture is nicely browned; adjust seasoning as needed.
Spoon about 1/4 cup marinara into the bottom of a 9x13 baking dish. Layer half the zucchini slices over the sauce, spread half the mushroom mixture over the zucchini, top with half the remaining marinara, then sprinkle half the Parmesan and half the shredded mozzarella.
Repeat the layers with the remaining zucchini, mushroom mixture, marinara, Parmesan, and mozzarella.
Bake the assembled lasagna until the cheese is browned and bubbly, about 40 minutes; cover with foil if it browns too quickly, or finish under the broiler 1–2 minutes if more browning is desired.
Remove from the oven and let rest a few minutes before cutting. Garnish with chopped basil and additional Parmesan if desired.