Preheat the oven to 425 degrees F with a sheet pan on the middle rack.
In a large bowl, toss the asparagus and mushrooms with olive oil, 1/2 teaspoon kosher salt and 1/4 teaspoon black pepper.
Carefully spread the asparagus and mushrooms across the hot sheet pan. Roast for 12-15 minutes, flipping halfway through roasting. The asparagus should be bright green and the mushroom should be lightly browned. Take them out of the oven and toss the vegetables with garlic and scallions on the pan.
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 asparagus & mushrooms, half the spinach, half the feta cheese and half the herbs into the pie dish.
Pour in the egg mixture. Top with the remaining asparagus & mushrooms, spinach, feta, chives and parsley.
Bake for 40-45 minutes until just set in the middle and lightly browned on top.