Step 1

Preheat the oven to 400°. With the side of a large knife, mash the garlic cloves with 1 tablespoon of kosher salt to make a coarse paste. Transfer the paste to a small bowl. Stir in the coriander, thyme, oregano, 1 tablespoon of salt, 2 tablespoons of coarsely ground black pepper and 1/2 cup of the olive oil until incorporated.

Step 2

On a work surface, rub the garlic-herb oil all over the butterflied pork. With the fatty side up, fold the pork under itself into thirds and transfer to a roasting pan. Roast the pork for 40 minutes. Reduce the oven temperature to 300° and roast the pork for about 2 hours and 20 minutes longer, until an instant-read thermometer inserted in the center registers 160°.

Step 3

Meanwhile, bring a large saucepan of salted water to a boil. Add the fava beans and boil until the skins loosen, about 2 minutes. Using a slotted spoon, transfer the favas to a work surface; peel off and discard the tough skins and transfer the favas to a bowl. Alternatively, boil the frozen edamame for 2 minutes and transfer to a bowl. Add the carrots to the saucepan and boil until tender, about 4 minutes. Using a slotted spoon, transfer the carrots to the bowl. Add the peas and cook until tender, about 2 minutes; if using frozen, boil just until hot, 30 seconds. Drain the peas and transfer to the bowl.

Step 4

In the same saucepan, melt the butter in 1 tablespoon of the olive oil. Stir in the vegetables and season with salt and pepper. Cook over moderate heat until just heated through. Stir in the 3 tablespoons of chopped herbs.

Step 5

Transfer the pork to a carving board and let rest for at least 10 minutes. Strain the pan juices into a small saucepan and skim off the fat. Add the remaining 2 tablespoons of olive oil and balsamic vinegar and season with salt and pepper. Bring to a simmer, cover and keep hot.

Step 6

Thickly slice the pork across the grain and transfer to plates. Serve with the vegetables, passing the sauce at the table.