Preheat the oven to 400°F (200°C).
Roll out the puff pastry on a floured surface to about 1/8 inch thickness and transfer it to a baking sheet lined with parchment paper.
In a skillet over medium heat, add olive oil and sauté the asparagus for 2-3 minutes until slightly tender.
Add the peas and cherry tomatoes to the skillet and cook for an additional 1-2 minutes. Season with salt and pepper.
Arrange the cooked vegetables over the pastry, leaving a 1-inch border around the edges. Sprinkle the goat cheese and basil over the top.
Fold the edges of the pastry over the filling slightly, and brush the edges with the egg wash.
Bake in the preheated oven for 25-30 minutes, until the pastry is golden brown.
Allow to cool slightly before slicing and serving. Enjoy your Spring Vegetable Galette!