Place the sweetbreads in a bowl of cold water and refrigerate for 45 minutes to 1 hour, changing the water once or twice, until it runs mostly clear.

Bring water to a bare simmer in a 3-quart / 2.8L saucepan with the vinegar, bay leaf, peppercorns and 1 tsp salt.

Slide in the sweetbreads and poach gently for 3 to 4 minutes, until firm but still yielding when pressed. Lift straight into a bowl of ice water.

Once cool enough to handle, peel away the outer membrane and any visible tubes or dark veins with a paring knife, working over a bowl since bits pull away easily.

Sandwich the peeled sweetbreads between two plates, weigh the top plate down with a couple of cans, and refrigerate for 30 to 45 minutes. This flattens them so they slice evenly and hold together in the pan; skip it and the slices crumble when you try to turn them.

Slice the pressed sweetbreads into 1.5 cm / 5/8-inch medallions. Season both sides with salt and pepper.

Dredge each piece lightly in flour, shaking off the excess.

Melt half the butter with the olive oil in the 12-inch / 30cm skillet over medium-high heat until the foam subsides.

Add the sweetbreads in a single layer, working in batches so the pieces don't touch, and sear for 3 to 4 minutes per side until deep golden and an instant-read thermometer reads 165 F / 74 C at the center.

Transfer the seared pieces to a plate. Add the remaining butter and sage leaves to the skillet and let the butter turn nutty and the sage crisp, about 1 minute.

Off heat, stir in the lemon juice and capers, scraping up any browned bits from the pan.

Spoon the sage butter over the sweetbreads, scatter with parsley, and serve right away with lemon wedges.