Heat oven to 325°F. Season brisket with salt and pepper and brown in oil in a snug Dutch oven for 4 minutes per broad side.
Lift out beef, soften onion in the pot for 5 minutes and add stock and thyme. Return beef, cover tightly and braise for 3 to 3 1/2 hours until a fork slides in easily, usually around 195–205°F; add a little extra stock if the pot starts drying.
Rest beef for 15 minutes and pull into broad pieces, discarding firm fat seams. Strain the cooking liquid, discard spent onion and skim the fat; measure 2 cups, reducing excess liquid or adding a little water if needed.
Brown mushrooms in butter in a skillet over medium-high heat for 8 to 10 minutes. Stir in flour for 1 minute, then gradually whisk in the measured braising liquid.
Simmer gravy for 5 minutes until it coats a spoon. Add brisket and heat gently until steaming hot throughout.
Toast rye on both sides under the broiler for 1 to 2 minutes total. Put one slice on each plate, divide brisket and mushroom gravy over it and serve immediately as four open-faced sandwiches.