Set the Instant Pot to sauté and melt the butter in the insert. When the butter has melted and begins to foam gently, it is ready for the mushrooms.
Add the mushrooms and garlic, then cook until the mushrooms are deeply browned; stir in the thyme or sage, salt, and pepper for the final 30 seconds, then turn off the sauté setting. The herbs should smell fragrant and the mushrooms should have golden brown edges with flavorful browned bits on the bottom.
Season the chicken thighs with salt and pepper, arrange them over the mushroom mixture, and pour in the broth; lock the lid and cook on manual high pressure for 5 minutes. The chicken cooks above the mushroom layer while the broth captures the buttery garlic flavor below.
Allow the pressure to release naturally for 5 minutes, then carefully vent the remaining pressure before opening the lid. This gradual release helps the chicken stay tender instead of tightening abruptly.
Transfer the chicken to a plate with a slotted spoon, leaving the mushrooms and cooking liquid in the pot; whisk in the heavy cream and Dijon, then use sauté to gently thicken the sauce for a few minutes. The sauce should bubble softly and begin to cling lightly to the back of a wooden spoon.
Scoop out about half a cup of warm liquid, whisk in the glucomannan or xanthan gum until smooth, then stir the mixture back into the pot and return the chicken. As the sauce thickens, it should look glossy and rich with no visible lumps around the mushrooms.