Braised Shallot & Grana Padano Agnolotti Filling

Heat the oven to 325°F. Trim the roots of the shallots but leave the base intact to keep the layers together. In a shallow Dutch oven or medium sauté pan, melt the butter over medium-high heat. Add the shallots, cut-sides down, and sprinkle with salt. Cook until they begin to caramelize, 3 to 5 minutes. Turn down the heat if the butter starts to brown too quickly. Pour in the vermouth, scraping up any browned bits, and simmer until reduced by half, about 3 minutes. If you’re using a sauté pan, transfer the shallots and liquid to a baking dish (otherwise, keep them in the Dutch oven). Add the stock, cheese rind, thyme, and a generous pinch of salt. Cover with foil and braise in the oven until the shallots are very tender, about 45 minutes. When done, let them cool completely. Strain the braising liquid to use as the sauce later. Cut off the roots from the cooled shallots, remove any tough outer layers, and pat dry. Roughly chop and add to a food processor, then pulse until fine. Add the cheeses and pulse again, then adjust seasoning to taste with salt, pepper, and lemon juice. Transfer to a piping bag and chill thoroughly before use.