In a large bowl whisk together the eggs, dairy product, cheese, salt, and pepper, and just until the egg yolks and whites have combined.
Add oil to a 12", oven safe skillet and heat over medium. Once shimmering, add the veggies and sauté until most of the water has been removed. Note: If you're using both dense and soft veggies, (dense: onion, soft: mushrooms), saute dense vegetables first and allow them to soften before adding the softer varieties. If adding garlic, do so at the very end and only saute until fragrant. Salt and pepper your veggies to taste.
Whisk your egg combo once more to incorporate everything that has settled, then pour it over the veggies. Use a spatula to spread everything evenly across the pan, and to slightly lift the veggies along the bottom and sides so the eggs can settle around them.
Reduce the heat of your pan to low, and nestle a lid on top. Continue to cook your frittata for 11-14 minutes, or until it has set around the edges, the very center should still jiggle slightly. Meanwhile, turn your oven broiler to high, and position the top rack so that it's 10" from the bottom of the heating element.
Finish your frittata under the oven broiler--you'll know it's done once the center is set and the top is golden, should be 2-3 minutes. Enjoy!