Combine flour and eggs in a processor or bowl until the mixture looks like breadcrumbs.
Knead the mixture on a floured surface for 3 minutes until smooth.
Wrap the dough in film and chill in the refrigerator for 20 minutes.
Mix the ricotta, Parmesan, and herbs in a bowl and season with salt and pepper.
Roll the pasta dough very thin using a rolling pin or a pasta machine.
Cut the pasta sheets into 7.5 cm squares.
Brush square edges with water and place a spoonful of filling in the center.
Fold each square into a triangle and press the edges firmly to seal.
Bring the two long-edge corners of the triangle together and press to join.
Purée basil, garlic, and Parmesan, then blend with olive oil to make pesto.
Boil the peas and beans for 4 minutes until tender, then drain and add to the pesto.
Boil the pasta in batches for 2 minutes and transfer to the pesto pan.
Add a little pasta water to the pan and heat through while stirring gently.
Serve in bowls topped with more Parmesan and mint sprigs.