Slice the carrots into 1/4-inch rounds, cut the celery into 1/4-inch pieces, and dice the onion into 1/2-inch pieces. Halve or quarter the potatoes depending on their size, aiming for roughly uniform pieces so they cook evenly. Cut the chicken breasts into 1-inch chunks. Having all your prep work done before assembly ensures the slow cooker can start cooking immediately and helps everything cook at the same rate.
In a bowl, whisk together the chicken broth, Worcestershire sauce, tomato paste, minced garlic, poultry seasoning, black pepper, salt, dried rosemary, and thyme. Whisking the tomato paste into the liquid prevents lumps and ensures the flavors distribute evenly throughout the stew. I find that freshly minced garlic gives noticeably better flavor than pre-minced, so take the extra minute if you can.
Add the chicken chunks, diced onion, sliced carrots, halved potatoes, and sliced celery to your slow cooker, then pour the braising liquid from Step 2 over top. Place the bay leaves on the surface. Cook on low for 7-8 hours or on high for 4-5 hours, until the chicken is very tender and the potatoes are fully cooked through. The long, gentle cooking breaks down the chicken and vegetables while developing deep, complex flavors.
While the stew finishes cooking, whisk the cornstarch with the milk in a small bowl until completely smooth with no lumps—this prevents the cornstarch from clumping in the hot liquid. In the final 20 minutes of cooking, stir the cornstarch slurry and frozen peas into the slow cooker. The stew will thicken noticeably as the cornstarch cooks and activates. Remove and discard the bay leaves before serving.