Training in French kitchens and traveling in Europe made me fall in love with both celery root and sweetbread cookery. Celery root is a flavorful root vegetable and is super versatile. Pink Lady apple adds a lovely natural sweetness to this elegant dish.
The day before cooking the sweetbreads, place them in a nonreactive bowl, cover with the milk, and allow them to soak in the refrigerator to remove any residual blood and impurities. The next day, discard the milk, then trim any veins or discoloration from the sweetbreads. Rinse them well and set aside.
Put the sweetbreads in a pot, cover with water, and add the salt. Bring the water up to a low simmer, then cook for about 5 minutes. Remove the sweetbreads and plunge them into an ice bath. Clean off any tough membranes and fat. Line two quarter-sheet pans with clean kitchen towels in a single layer. Fold the towels over the sweetbreads to cover, then place another quarter-sheet pan on top, and weigh down with a heavy pot. Place in the refrigerator to chill for 1 to 2 hours.
For the celery root salad: Whisk the mayonnaise, parsley, capers, Dijon, vinegar and Espelette pepper together in a bowl. Fold in the celery root, celery seeds and apple. Set aside.
Prepare the seasoned flour by whisking together the instant flour, salt and white pepper. Cut the sweetbreads into pieces about 3 inches across. Toss the sweetbreads in the seasoned flour. Set aside.
Melt the clarified butter in a 12-inch, heavy-bottomed cast-iron skillet. Add the floured sweetbreads, garlic cloves, bay leaves and shallot. Add the unsalted butter and cook the sweetbreads over medium heat, flipping halfway through and basting as the butter melts, until golden brown, about 8 minutes. Place the sweetbreads on a paper towel-lined tray and set aside. When ready to serve, slice.
Plate the celery root salad, then top with the crispy sweetbreads, some of the browned butter and the celery leaves. Garnish with more capers and sprinkle with Espelette pepper.