Turn on a multi-functional pressure cooker (such as Instant Pot®), add butter, and select Saute function. Add chicken thighs to melted butter and sear, 4 to 5 minutes per side. Remove chicken and set aside.
Add carrots, onion, and celery; cook until onions begin to soften, about 5 minutes. Add garlic and saute until fragrant, about 1 minute. Add 1/2 cup chicken broth and stir to deglaze the pot.
Add chicken thighs back to the pot along with remaining chicken broth, flour, Worcestershire sauce, bay leaves, poultry seasoning, thyme, pepper, rosemary, and salt. Stir together, then close and lock the lid.
Switch to high pressure according to manufacturer’s instructions; set timer for 10 minutes. Allow 10 to 15 minutes for pressure to build.
Release pressure using the natural-release method according to manufacturer’s instructions for 10 minutes. Release remaining pressure carefully using the quick-release method according to manufacturer’s instructions, about 5 minutes. Unlock and remove the lid.
Remove chicken and shred or cut into bite-sized pieces. Return to the pot. Remove and discard bay leaves.
Set cooker to Saute. Add heavy cream and bring to a boil. Add frozen peas to boiling stew and cook, stirring as needed, until heated through, about 5 minutes.
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