Turn your oven to 400°F and line a baking sheet with parchment paper. This step matters more than it seems, since a hot oven from the start is what gives the pastry its crisp, golden lift. While the oven heats, gather your ingredients so everything is within reach.
Lightly roll the thawed puff pastry sheet into roughly an 11-inch square, then slice it in half to make two rectangles. Transfer both pieces onto the lined baking sheet and bake for about 8 minutes. This par-bake gives the pastry a head start so the base doesn't turn soggy later.
While the pastry bakes, warm the olive oil in a large skillet over medium heat. Add the spinach and minced garlic, season with salt and pepper, and cook for about 2 minutes, stirring often. You're just looking for the spinach to fully wilt down.
Once the spinach has wilted, stir in the crumbled feta and let it cook for another 30 seconds so it softens slightly into the greens. Pull the skillet off the heat once it's combined. This filling should smell garlicky and a little salty already.
Take the par-baked pastry out of the oven and use a fork to gently press down the center of each piece, leaving about a 1½-inch puffed border around the edges. Divide the spinach and feta filling evenly between the two pastries, spreading it into that pressed-down center.
Make a small well in the middle of the filling on each pastry and crack one egg directly into it. This is what gives the tart that beautiful golden, slightly jammy center once it bakes.
Slide the tray back into the oven and bake for 10 to 12 minutes, until the pastry is a deep golden brown and the egg white has set. Keep an eye on it near the end so the yolk doesn't overcook if you like it runny.
Let the tart rest for about 3 minutes once it's out of the oven this helps everything set just slightly so it's easier to cut. Slice each piece into wedges, sprinkle over a little extra feta if you like, and serve warm.