Preheat oven to 425 degrees. Prepare a baking sheet with foil and cooking spray.
Halve and peel onion. Cut half of the onion into 1/4" dice. Set aside the other half as you will not need it.
Mix cornstarch and ¼ cup water in a large mixing bowl.
Heat a large non-stick pan over medium-high heat. Add 2 tsp. olive oil and diced onion to hot pan, and cook until softened, 2-3 minutes. Add spinach and cook until wilted, 2-3 minutes. Stir in cornstarch mixture. Remove from burner and transfer spinach filling to mixing bowl used for cornstarch mixture. Season with ¼ tsp. salt. Let filling rest until it is cool to the touch.
Once spinach filling has cooled to the touch, add ricotta, feta, 1/2 tsp. oregano, and ¼ tsp. salt to bowl. Mix thoroughly.
Place one puff pastry square onto prepared baking sheet. Scoop spinach filling onto dough center, leaving ¼" border. Lightly brush dough border with water. Gently stretch second puff pastry square ¼" in each direction, and cut a vent in the middle. Place dough square over filling, meeting first dough square. Use a fork to crimp and press dough pieces together. Brush top with 1 tsp. olive oil.
Bake until tart is puffed up and browned, 16-20 minutes. Remove from oven and rest 3-5 minutes.