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1
2 days before cooking, place the sweetbreads in a bowl or small container, cover them with milk, and allow them to soak in the refrigerator overnight. Remove the sweetbreads, discarding the milk, and trim any veins or dark bits. Rinse them well and set aside.
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2
Place the sweetbreads in a small pot, cover with water, and add a big pinch of salt and the juice of half a lemon. Add the sweetbreads, bring the water to a boil, and blanch them for about 5 minutes. Remove the sweetbreads and plunge them into an ice bath.
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3
Line a small sheet pan with a kitchen towel and place the sweetbreads on the towel in a single layer. Fold the towel over them to cover, place another sheet pan on top, and weight it down - a heavy pot or a few cans of tomatoes work well. Place in the refrigerator overnight.
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4
If your sweetbreads are large, slice them into medallions. Spread the flour on a plate and season with lots of salt and pepper, then toss the sweetbreads in the seasoned flour until well coated on all sides.
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5
Melt the butter in a heavy bottomed skillet and cook the sweetbreads over medium heat until golden brown. Place the browned sweetbreads on a paper towel-lined plate and set aside, tenting loosely with foil to keep warm.
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6
Whisk the tablespoon of lemon juice with a pinch of salt, a few grinds of pepper, and the olive oil in a small bowl until emulsified. Add the capers, celery leaves and parsley and stir to combine. Place the sweetbreads on a serving plate, and drizzle the sauce all around. Finish with a little flaky salt if desired.
