Allow the eggs and frozen puff pastry to sit at room temperature for 30 minutes.
Preheat the oven to 400ºF and line a baking sheet with parchment paper.
Once the puff pastry has thawed, unfold it onto a lightly floured work surface, and using a rolling pin, roll it into a 14x11-inch rectangle. Using a sharp knife, score a 1/2-inch border around the edges. Transfer the pastry to the baking sheet then prick it several times with a fork. Bake it for about 10 minutes, or until it's lightly golden brown. Remove it from the oven.
Add the olive oil to a large sauté pan set over medium heat. Add the garlic, asparagus and peas to the pan and cook, stirring, for 2 to 3 minutes until the garlic is golden brown.
Season the mixture with salt and pepper then transfer it onto the baked puff pastry, spreading it evenly within the edges.
Break the eggs, one at a time, into a small dish then carefully pour each egg onto the tart, spacing them evenly apart. Sprinkle each egg with fresh black pepper then bake the tart for 12 to 14 minutes just until the egg whites are completely cooked and no longer translucent.
Remove the tart from the oven, sprinkle it with the crumbled goat cheese, chopped fresh chives and Parmesan cheese. Slice and serve the tart immediately.
To brighten the color of the asparagus and peas, blanch them in boiling water for 30 seconds then immediately transfer them to a bowl of ice water. Dry the asparagus thoroughly before sautéing them and continuing with the recipe as directed.