Position a rack in the center of the oven and heat the oven to 450°F. In a medium bowl, whisk the eggs, crème fraîche or cream, chopped dill, lemon zest, salt, and about 10 grinds of pepper.
On a lightly floured surface, gently roll out the puff pastry until it measures about 11 by 13 inches. Line a rimmed baking sheet with parchment or a silicone baking mat. Lay the pastry on the baking sheet, wet the edges with water, and fold over a 3/4-inch border, mitering the corners for neatness. Distribute the feta evenly within the border, and then carefully pour the egg mixture over the cheese, taking care that it doesn't slosh onto the border. Carefully transfer the baking sheet to the oven and bake until the pastry is puffed and brown on the border and the underside, and the filling is golden brown, 18 to 20 min.
Slide the galette off the pan and onto a rack to cool until still warm but not hot. Move the galette to a cutting board and cut into four rectangles, so that each piece gets some border. Put the four pieces on plates.
In a large bowl, toss the spinach and dill sprigs (if using) with the olive oil and lemon juice until evenly coated. Sprinkle with salt, pepper, and more lemon juice to taste. Arrange a handful of salad on each piece of galette and serve immediately.
Thaw puff pastry in the refrigerator overnight or all day while you’re at work. Or thaw at room temperature for at least 45 minutes (less if your kitchen is quite warm).