Make a bouquet garni: Wrap smashed garlic, peppercorns, bay leaf, thyme sprigs, and parsley stems in a piece of cheesecloth; tie with kitchen twine.

Season chicken with salt and pepper. Place flour in a shallow dish and dredge chicken, shaking off any excess.

Heat butter and 1 tablespoon oil in a 6-to-8-quart stovetop pressure cooker over medium, or in an electric pressure cooker set to saute.

Working in batches, add chicken and cook until golden brown on both sides, 3 to 4 minutes; transfer to a plate.

Add remaining 1 tablespoon oil to cooker; increase heat to medium-high.

Add mushrooms, onions, and minced garlic. Season with salt and pepper; cook until golden, about 6 minutes. Transfer mixture to plate.

Add cognac and wine to cooker. Using a wooden spoon, scrape up any browned bits and cook until reduced by half, about 4 minutes.

Add broth (2 ¾ cups for stovetop; 2 ¼ cups for electric), tomato paste, bouquet garni, and reserved chicken and mushroom mixture; bring to a boil.

Stovetop: Secure lid. Bring to high pressure over medium-high heat; reduce heat to maintain pressure and cook 10 minutes. Remove from heat and quickly release pressure, then remove lid.

With a slotted spoon, transfer chicken, mushrooms, and onions to a bowl. Remove and discard bouquet garni. Return cooker to medium-high heat.

Electric: Secure lid. Manually set cooker to 14 minutes and let it come to pressure. Once time is complete, turn off and quickly release pressure, then remove lid.

With a slotted spoon, transfer chicken, mushrooms, and onions to a bowl. Remove and discard bouquet garni. Set cooker to saute.

Bring liquid to a boil and cook until reduced by half, about 7 minutes.

Return chicken, mushrooms, and onions to cooker; cook 2 minutes. Skim any fat from surface; season with salt.

Stir in parsley leaves, top with thyme leaves, and serve.