Line a baking sheet with parchment paper and place the 6 squares of puff pastry on the sheet. They should be approximately 4 1/2 inches square and about 1/4 inch thick.
Now if you want to keep things really simple, you can just prick the pastry with a fork, leaving a 1/2 inch rim around the edge, or carry on for directions for the pretty edges. I find it easiest to work with the pastry while it is still slightly frozen.
Fold one of the edges of the pastry square to the opposite edge to make a triangle. Leaving a 1/4-inch border, cut about 3/4 of the way from the bottom of the triangle to the tip on both sides, making sure the cuts do not touch. Unfold the square. Brush the inner edges with beaten egg. Take the top flap and fold it toward the 2 cuts near the bottom. Then take the bottom flap and fold it toward the top edge. You will have a diamond shape. (This video shows the method simply.) Repeat with all 6 squares.
Mix 2 tablespoons of pesto with the ricotta and 2 teaspoons of lemon juice. Season well with salt and pepper, then divide between the 6 tarts. Spread around the bottom of the tarts.
Cut the asparagus into 2-inch pieces. Thinly slice the radish. In a medium bowl, stir together the remaining tablespoon of pesto, teaspoon of lemon juice and olive oil. Mix well, then add vegetables and toss to coat. Season well, then divide among the tarts. Heap up the vegetables, pressing them into the ricotta.
Place the pan in the refrigerator and chill for 15 minutes (or may hold for up to 4 hours). Preheat oven to 400F.
Bake tarts, rotating the pan occasionally, until dark brown and crispy, about 25-30 minutes. Serve hot with additional ricotta if desired.