For the cappellacci, place the flour and eggs into a mixing bowl or the bowl of a food processor. Either rub the wet ingredients into the dry ingredients using your fingertips or blitz until the mixture resembles breadcrumbs.
Turn out the mixture onto a lightly floured work surface and bring it together as a dough. Knead lightly for 2-3 minutes until smooth and elastic.
Wrap the dough in cling film and chill in the fridge for 20 minutes.
Meanwhile, mix the ricotta, Parmesan and herbs in a bowl until well combined. Season, to taste, with salt and freshly ground black pepper. Set aside or chill until needed.
When the pasta has chilled, roll it out on a lightly floured work surface until very thin using a rolling pin. Alternatively, dust the rollers of a pasta machine with flour and feed portions of the pasta dough through the rollers, working from the widest to the narrowest setting, reducing the machine by one setting each time the pasta sheet is passed through it.
Cut a series of 7.5cm/3in squares from each sheet of pasta using a sharp knife.
Brush the edges of each pasta square with a little water and place one spoonful of the ricotta mixture into the centre of each.
One by one, pick up one corner of each pasta square and fold it over the filling to meet the opposite corner. Press the edges of the pasta together to seal, creating a triangular shaped parcel.
Gently squash the filling of each parcel slightly to fill the space. Bring the tips of the long edge of each triangle together, then press to hold in place. Repeat the process with all of the filled pasta squares.
For the pesto, blend the basil, garlic and Parmesan to a fine purée in a food processor. Pour in the olive oil and blend again until smooth. Season, to taste, with salt and freshly ground black pepper. Transfer the pesto to a frying pan and set aside.
Bring a large saucepan of salted water to the boil. Add the peas and beans and simmer for 3-4 minutes, or until tender. Drain well and add to the frying pan with the pesto.
Bring a fresh batch of salted water to the boil in the same saucepan. Cook the cappellacci in batches for 1-2 minutes, or until they float to the surface of the water, then remove from the pan using a slotted spoon and transfer to the pan containing the pesto. Repeat the process with the remaining cappellacci.
Add a couple of spoonfuls of the pasta water to the frying pan containing the pesto. Heat until the mixture is warmed through, stirring carefully to combine.
To serve, divide the cappellacci and pesto among serving bowls and sprinkle with extra grated Parmesan. Garnish with a few sprigs of mint.