Tip: dice raw bacon as soon as you pull it out of the refrigerator. Cold bacon is much easier to cut.
Prepare bacon and vegetables and set aside. Grate cheese if needed and set is aside.
Preheat a large cooking pan over medium-high heat and add oil.
Add diced bacon and cook, stirring from time to time, until bacon fat is rendered about half way.
Stir in diced shallot and cook bacon and shallot together until the fat is mostly rendered. Strain off excess bacon fat.
Stir in mushrooms and cook until mushrooms are mostly done and add chopped spinach. Cook for another minute or two, until spinach is wilted.
Drain off excess juices from the filling so that it doesn't make the quiche too thin. Set the filling aside to cool for a few minutes.
In a mixing bowl, whisk together eggs, milk, salt, and pepper until smooth.
Preheat the oven to 350°F and grease a deep round baking dish (you can use a deep 9-inch pie dish).
Mix the filling into the egg mixture once it's cooled for a few minutes and spread the mixture in the prepared baking dish.
Spread grated cheese over the top and gently press it down to mostly be covered with the egg.
Bake quiche for 40-45 minutes. Let it rest for at least 15 minutes before cutting.
Notes
Make ahead: you can easily prepare the filling ahead of time and store it in the refrigerator for a day or so, until ready to prepare the quiche. You can also make the whole quiche ahead of time, cover it air-tight, and refrigerate overnight. Bake it the next day as directed but let the baking dish sit on the counter for about 30 minutes to warm up before baking.
Storing: it's easy to store leftover crustless quiche in the same baking dish, just make sure it's cooled and cover it air-tight. Store it in the refrigerator for 2-3 days.