In a shallow bowl, mix 1 cup flour, 1/2 teaspoon black pepper, 1 teaspoon dried sage and salt to taste.
Sprinkle additional salt to taste on the 2 1/2 pounds skinless, bone-in chicken pieces (if desired), then dredge each piece in the seasoned flour to coat; shake off excess flour.
Heat 1/4 cup oil in a large skillet over medium-high heat.
Add the floured chicken to the hot skillet and lightly brown on both sides (about 3–5 minutes per side). Remove the chicken and place on a paper-towel–lined plate to drain.
In the same skillet, add the thinly sliced yellow onion and sauté until tender, about 4 minutes.
Add the 2 minced garlic cloves to the skillet and sauté for 1 additional minute.
Transfer the sautéed onion and garlic to the slow cooker. Add the 3 sliced carrots, the 1 cubed potato, and the 2 sliced celery stalks to the slow cooker.
Place the browned chicken on top of the vegetables in the slow cooker. Pour in 2 cups chicken broth.
Add additional salt and black pepper to taste, if desired. Cover and cook on low for 6–8 hours, until the chicken is falling off the bone.
Stir in 1 cup frozen peas during the last 15 minutes of cooking, cover, and continue cooking for 15 minutes.
Before serving, taste and adjust seasoning as needed; remove chicken from bones and serve.