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1
Heat the oven to 160 °C. Tie a length of kitchen string around the circumference of each shank to hold the meat against the bone during braising. Season generously on both sides, then dredge in flour, shaking off all excess. The shanks are ready when they carry only a thin, even film of flour.
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2
In a heavy casserole wide enough to hold all four shanks in a single layer, heat the butter and oil together over medium-high heat until the butter foam subsides. Place the shanks in the pot without crowding and brown for 3–4 minutes per side. They are ready to turn when they release cleanly from the base and show a deep, even golden crust.
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3
Remove the shanks and set aside. Reduce the heat to medium. Add the diced onion, carrot, and celery to the same pot and sweat, stirring occasionally, for 8 minutes. The vegetables are done when they are fully soft, translucent, and carrying the colour of the fond without having browned.
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4
Pour in the white wine and raise the heat. Scrape the base of the pot thoroughly to lift the fond into the liquid. Reduce the wine by half; the sharp alcohol smell will give way to a softer, rounded aroma that signals the reduction is complete.
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5
Add the stock, tomato paste, bouquet garni, strip of lemon zest, and the two lightly crushed garlic cloves. Stir to combine. Return the shanks to the pot in a single layer. The braising liquid must reach at least two-thirds up the sides of the shanks. This is where the dish lives or dies: shanks stacked rather than lying flat in a single layer, or submerged in too little liquid, will cook unevenly and the marrow will seize rather than tremble. Cover with a tight-fitting lid and transfer to the oven.
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6
Braise for 2 to 2.5 hours, turning the shanks once at the halfway point. At the end of cooking, test by pressing the meat gently with a spoon: it should yield completely and be tender enough to cut with a spoon, yet still cling to the bone. The sauce should have reduced and thickened naturally from the flour coating and the melted marrow fat. If the sauce remains thin, remove the shanks, reduce the liquid briefly on the stovetop, then return them.
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7
Lift the shanks carefully onto a warm serving dish or back into the pot. Remove and discard the string, bouquet garni, lemon zest strip, and garlic cloves. Combine the chopped parsley, minced garlic, and grated lemon zest to make the persillade. Scatter it generously over the shanks at the moment of service. The persillade is ready when the lemon fragrance rises sharply against the warm, unctuous braise.