If your brisket is too large to sit flat on the bottom of your pressure cooker, cut it into pieces that will fit. Season brisket all over with salt and pepper.

In an electric multi-cooker (such as an Instant Pot), set to searing mode or a stovetop pressure cooker set over medium-high heat, add oil and heat until shimmering.

Working in batches, add brisket, and brown on both sides, about 6 minutes per side. Transfer brisket to platter or rimmed baking sheet, and set aside.

Add 1 to 2 tablespoons additional oil, as needed, if pot has gone dry. Add onion, carrot, celery, and garlic, and season with salt. Cook, stirring and scraping up any browned bits, until onions are very soft and any released juices have thickened into a glaze, 25-35 minutes.

Stir in ketchup and tomato paste and cook, stirring, until thick, about 3 minutes. Add wine and cook until raw alcohol smell has cooked off, about 3 minutes.

Add thyme and bay leaves. Reduce heat to medium-low or turn off searing mode on electric multi-cooker. Give the vegetables a good stir, scraping the bottom well all over.

If vegetables are very dry, stir in ½ cup water to moisten. Add brisket pieces, nestling them well in the vegetables, and add any accumulated juices.

Seal pressure cooker and bring to high pressure over medium heat or using the pressure-cooking mode of an electric multi-cooker. Cook for at least 1 hour at high pressure and up to 1 hour 30 minutes.

Rapidly release pressure cooker or allow to release naturally, then open. Transfer brisket pieces to a work surface, and let rest until cool enough to handle.

Taste braising liquid and season with salt, if necessary. Discard thyme sprigs and bay leaves, and skim off any excess fat if it's there.

If the braising liquid is a little too watery, you can reduce it at this point by simmering it uncovered until it thickens slightly.

Slice brisket thinly against the grain. Arrange on a platter and spoon the sauce and vegetables all over. Cover and let stand for 30 minutes in a warm place. Serve.