Season chicken pieces with salt and pepper, then dust lightly with flour, shaking off the excess.
Heat vegetable oil in pressure cooker or skillet over medium-high heat. Add butter. Sear chicken skin-side down in batches until golden brown, about 4–5 minutes per side. Set aside.
Reduce heat to medium. Add another tablespoon of butter, then onions. Cook 3–4 minutes until starting to soften.
Add sliced mushrooms, cook 6–8 minutes until browned and juices release.
Stir in garlic and cook 1 minute until fragrant. Add chicken back into pan.
Pour in brandy and wine, scraping up any browned bits. Simmer to reduce slightly.
Stir in tomato paste, then add beef stock, salt and pepper.
Bring to simmer, close lid and cook under pressure for 25–30 minutes. Then natural release for a few minutes followed by quick release.
Optional: Simmer uncovered for 5–10 minutes to thicken sauce.
Finish with cold cubed butter and tarragon stirred in gently. Serve hot.
Notes
Serve hot with creamy mashed potatoes, rice or small pasta. Leftovers reheat well and can be frozen for up to 3 months.