Preheat the oven to 425°F. Grease a 9x13-inch baking dish with cooking spray.
Heat the olive oil in a small saucepan. Add the garlic and oregano and cook for 1 minute, until fragrant. Add a pinch of chile flakes and cook for 1-2 minutes. Stir in the crushed tomatoes and bring to a simmer for 20 minutes. Season with salt and pepper.
On a baking sheet, toss the mushrooms with 1 tablespoon olive oil, half of the minced garlic, and a pinch of salt and pepper. Roast until brown, 10-15 minutes.
Heat a large skillet over medium heat with the remaining olive oil. When hot, add the remaining garlic and chile flakes and cook until golden, 1 minute. Add the kale and sauté for 2-3 minutes, until just wilted.
Bring a large pot of salted water to a boil. Add the lasagna noodles and cook according to package instructions. Drain the pasta, return to the pot, and drizzle with olive oil.
To assemble the lasagna, spread a layer of tomato sauce on the bottom of the prepared baking dish, top with a layer of pasta, more sauce, kale and mushrooms, ricotta and mozzarella, pasta, sauce, and so on, finishing with a layer of cheese.
Cover with aluminum foil and bake for 20 minutes. Remove the foil and bake for 10 more minutes, until golden on top.
In a salad bowl, whisk together the olive oil, salt, pepper, vinegar, oregano and garlic. Fold in the remaining antipasto ingredients to combine.
Serve the veggie lasagna alongside antipasto.