Preheat the oven to 300 degrees . In a large dutch oven, heat 2 tablespoons olive oil over medium-high heat. Season the brisket with salt and pepper and add to the pot. Cook, turning once, until browned, about 10 minutes. Transfer to a platter.
Discard the fat in the dutch oven; add 2 tablespoons olive oil, the yellow onions, garlic, 8 sprigs thyme and the bay leaves; season with salt and pepper. Cook, scraping up the browned bits, until the onions are softened, about 5 minutes. Stir in the espresso and 1 cup water. Return the brisket, fat side up, and top with the onion mixture. Bring to a simmer, cover and transfer to the oven; braise until fork-tender, about 3 1/2 hours.
Transfer the brisket to a platter; let rest for 15 minutes before thinly slicing. Skim the fat from the cooking liquid and discard with the herbs. Simmer the liquid over medium-high heat until thickened, 5 to 10 minutes. Pour over the brisket.
In a large nonstick skillet, heat the remaining 1 tablespoon olive oil over medium heat. Add the pearl onions and cook for 5 minutes. Stir in the peas and remaining 3 sprigs thyme and cook for 3 minutes; season with salt and pepper. Discard the thyme. Serve the vegetables with the brisket.
