Using a spiralizer cut zucchini into noodles. Place zucchini noodles in a colander in the sink. Toss zucchini with 1 teaspoon salt. Let stand 20 minutes.
In a large skillet, heat oil over medium-high heat. Add tomatoes, oregano, and garlic; cook, stirring often, until tomatoes begin to wilt about 3 to 4 minutes. Remove mixture from pan; cool slightly.
Preheat oven to 375 degrees. Place half of zucchini noodles on a clean kitchen towel. Wrap towel around zucchini; twist and squeeze until all liquid is extracted. Repeat with remaining zucchini. Cut zucchini into manageable lengths.
In a large bowl, whisk eggs until lightly beaten. Whisk in milk, flour, pepper, and remaining 1/2 teaspoon salt. Add tomato mixture, cheeses, and zucchini; toss to combine.
Wrap bottom plate of a 9-inch springform pan tightly with foil. Assemble pan; coat bottom and sides with cooking spray.
Pour egg mixture into pan. Bake in preheated oven until the middle is set about 50-60 minutes.
Cool 10 to 15 minutes. Remove the sides from the pan; using a serrated knife cut the pie into 6 wedges.