Preheat your oven to 375°F. While it heats, spray a 9-inch pie pan lightly with cooking spray. Lay out your thawed puff pastry sheet and gently roll it to fit the pan, then press it in carefully and trim any excess from the edges. Set the prepared pan aside—don't worry about blind baking; the egg custard will keep the pastry from getting too soggy.
In a medium bowl, whisk together the room-temperature eggs, cottage cheese, milk, kosher salt, and black pepper until smooth and well combined. This custard is the foundation of your quiche—the cottage cheese adds richness and creaminess that makes each bite tender. Set the bowl aside until you're ready to pour.
Distribute the fresh spinach evenly across the bottom of your prepared pastry shell, using about half of it to create a base layer. Scatter the sun-dried tomato halves over the spinach, then add the torn basil leaves. Top with the remaining spinach to nestle the herbs and tomatoes in place. I find layering the greens on top helps them stay moist during baking rather than getting lost at the bottom.
Carefully pour the egg custard mixture from Step 2 over the layered vegetables, letting it flow evenly throughout the pan and settle into all the gaps. Sprinkle the crumbled feta cheese and freshly grated sharp cheddar cheese over the top, distributing them as evenly as possible. A light grinding of fresh black pepper over the cheese adds a professional finish and subtle bite to the final dish.
In a small bowl, whisk the single beaten egg until combined. Using a pastry brush, gently brush this egg wash along the visible edges and rim of the pastry crust—this creates that beautiful golden-brown finish you're after. Place the quiche in your preheated 375°F oven and bake for 35 to 40 minutes, until the center is just set (it should jiggle only slightly when you gently shake the pan) and the pastry edges are deep golden brown.
Remove the quiche from the oven and let it rest for 5 minutes before slicing. I like to let quiches rest briefly so the eggs fully set and the slices hold together cleanly. Cut into wedges and serve warm or at room temperature—this quiche is actually delicious either way.