Dice the celery, onion, carrots, and potatoes. The smaller the dice, the better! Trim any large pieces of gristle or fat from the chicken thighs, no need to remove every last bit though!
Melt butter in a large nonstick skillet over medium-high heat. Add the celery, onion, carrots, and garlic. Sauté, stirring occasionally, until soft, about 5-7 minutes.
Sprinkle the flour evenly over the veggies and stir constantly for 1 minute. Pour in the chicken broth and stir until thickened. Scrape everything into the CrockPot.
Add diced potatoes, seasonings, and chicken. Stir to combine, then press everything into an even layer. Use tongs to arrange the chicken in a single layer, smooth side down, with veggies on top and around.
Cover and cook on high for 2½–3½ hours or low for 3–5 hours, or until the chicken easily shreds.
When the chicken is almost done, bake or air fry biscuits according to package directions.
Remove the lid and transfer the chicken to a cutting board. Dice into small pieces, discarding any fat.
Return the chicken to the crockpot along with peas, corn, and heavy cream. Stir gently. Add the cheese a handful at a time, stirring until melted. If needed, cover and let it sit for a few minutes to melt fully. Thin with additional cream if needed.
Adjust seasoning if needed, adding ½ teaspoon more bouillon if desired. Spoon the mixture onto plates and top with a biscuit. Enjoy!
