Preheat the oven to 425 degrees F with a sheet pan on the middle rack.
In a large bowl, toss the broccoli and mushrooms with olive oil, 1/2 teaspoon kosher salt and 1/4 teaspoon black pepper.
Carefully spread the broccoli and mushrooms across the hot sheet pan. Roast for 12-15 minutes, flipping halfway through roasting. The broccoli should be bright green and the mushroom should be lightly browned. Take the pan out of the oven and toss the garlic and scallions with the vegetables on the baking sheet.
Reduce the oven temperature to 375 degrees F. Lightly grease a 9-inch pie dish with oil.
In a large bowl, whisk together the eggs, milk, 1/2 teaspoon kosher salt and 1/4 teaspoon black pepper and cottage cheese.
To assemble the egg bake, spoon about 3/4 of the roasted mushrooms & broccoli, half the spinach and half the parmesan cheese into the pie dish.
Pour in the egg mixture. Top with the remaining mushrooms & broccoli, spinach, parmesan and chives.
Bake for 40-45 minutes until just set in the middle.