If desired, start by cooking a slice of bacon: press the 'Saute' button to begin cooking at medium saute heat, and add the bacon once the cooker is hot. Cook until crispy, then set aside.
If the bacon did not render about 1 tablespoon of fat (or if you choose not to use bacon), add olive oil to coat the pan before adding the mushrooms. Season with a bit of salt and pepper and saute the mushrooms, stirring occasionally, until soft. Set the mushrooms aside in a large bowl (this bowl can later be re-used to mash the potatoes).
Add 1 more tablespoon of olive oil to the pot. Season the chicken pieces with salt and pepper, then add them to the cooker. Brown well on both sides, then set aside.
After removing the chicken, add the onions to the cooker and saute until they begin to soften and turn translucent. Add the wine, scraping the browned bits from the bottom of the pot to deglaze, and continue cooking on Saute Mode until the wine is reduced by half. Add the broth, carrots, thyme, and salt, then add the browned chicken back into the stew (along with any juices that settled on the plate).
Place a steamer basket on top of the chicken stew, and fill it with the quartered potatoes and garlic cloves. Cover the pressure cooker with the lid, ensuring that the valve is in sealing position. Cook under high pressure for 5 minutes (with Instant Pot, press ‘Cancel’ to stop saute mode before closing the lid, then press ‘Manual’ and "-" to select 5 minutes).
While the meal cooks, prepare the beurre manie: mix/mash the softened butter and flour together in a small bowl until they form a smooth paste.
When the cooking time is up, allow at least 10 minutes for the pressure to release naturally. Open the lid and carefully set aside the steamer basket. Using a fork, gently whisk the beurre manie into the stew to thicken it, then stir in the mushrooms. Rinse the bowl, then dump in the potatoes and garlic. Add the butter, milk and salt. Season both the potatoes and stew to taste, and serve topped with fresh parsley (and the crisped bacon, if desired).