Heat oven to 425F degrees. Prepare a 9-inch tart pan with removable bottom.
Line tart pan with pie crust, folding excess dough over to form double- thick sides. Prick bottom and sides with a fork. Place pan on cookie sheet and bake 7-9 minutes until set and very light golden around edges.
Meanwhile, heat oil in a large nonstick skillet. Add mushrooms and cook over medium heat, stirring occasionally, until tender (mushrooms will release their liquid), 4-5 minutes. Increase heat to medium-high and cook 1-2 minutes longer until liquid evaporates and mushrooms are light golden.
Scatter mushrooms over bottom of baked crust. Sprinkle with cheese.
Beat eggs, milk, salt and pepper in a small bowl with a fork until blended. Pour into crust.
Bake 15 minutes. Reduce oven temperature to 350F degrees and bake 10-15 minutes longer until filling is puffed and golden.