Put a large pot of salted water on the stove over high heat to boil.
Make basil pesto using a mortar and pestle: add garlic and salt, pound into a pulp; add pine nuts and pound to a paste. Add basil leaves gradually, crushing them in a circular motion to incorporate into the paste. Add cheeses, using the pestle to stir them into the paste, then slowly pour in the olive oil, stirring until you have a green paste. Transfer to a sterilised jar with lid.
Make the meatballs: to a large mixing bowl, add the pork mince, beef mince, minced onion and garlic, breadcrumbs, beaten egg, pepper, and 1 tablespoon basil pesto, and loosely combine with wet hands for a rustic texture. Use a spoon to scoop out the mince mixture, roll it loosely into a ball between two hands, using a digital scale to check each meatball is 20 grams, and repeat until mixture is finished.
In a large frying pan over medium-high heat 2 tbsp extra virgin olive oil and when shimmering place each meatball in the pan in a circular formation, so you remember the order you placed them. When finished, use tongs to turn the meatballs so they cook evenly, and continue turning every couple of minutes until they’re cooked through and browned all over, around 8-10 minutes.
While the meatballs are browning, add the spaghetti to the pot of salt boiling water, give it a stir to separate, and cook according to the packet instructions until al dente, around 8-9 minutes.
When the meatballs are cooked, transfer them to an oven tray and keep warm. Clean out the same frying pan with a paper kitchen towel, add a tablespoon of extra virgin olive oil, heat over medium until shimmering, add the small broccoli florets and peas and cook for a few minutes, stirring occasionally until tender but still bright green.
Push the green vegetables to one side of the pan, add another tablespoon each of extra virgin olive oil and basil pesto, add ½ cup of pasta water, and stir to create a sauce. Use tongs to transfer the cooked spaghetti to the same pan and stir to combine the lot. If you like, add a little more cooking water to make it saucier. Taste, and if needed, season with salt and pepper to suit your palate.
Add the meatballs to the pan and stir to combine, or, if your pan isn’t large enough, use tongs to distribute the pesto spaghetti and greens between bowls, top with meatballs, and sprinkle with a little more grated Parmigiano Reggiano. Or transfer to a large serving plate for the centre of the table. Serve with more cheese, fresh basil, salt and pepper, and a side salad.