Add red currant jelly, bayleaves, and thyme, then quince. Returnpork to pot, fat side up. Cover pot with foil,then lid; place in oven.
Braise pork until very tender andthermometer inserted into center registers165°F, basting occasionally, about 2 hours15 minutes. Cool pork uncovered at roomtemperature 1 hour. Chill uncovered untilcold, then cover and chill at least 1 day andup to 3 days.
Preheat oven to 350°F.
Transfer porkto work surface.
Cut off string.
Cut porkcrosswise into 1/2-inch-thick slices. Overlapslices in 13x9x2-inch baking dish. Usingslotted spoon, arrange vegetables andquince around pork. Boil juices in pot untilthickened enough to coat spoon, about 15minutes. Season with coarse kosher salt,pepper, and lemon juice to taste.
Pour overpork. Cover and bake until heated through,about 30 minutes.
Sprinkle pork with chopped mint;surround with lemon wedges and serve.
Quinces are ripewhen their peel changes from green toyellow. They should still be quite firm—soft quinces are rotten. Because they'reso hard, they can be difficult to prepare.First, use a vegetable peeler to remove theskin. Next, use a chef's knife to cut the fruitlengthwise (through the core) into wedges.With a small paring knife, carefully removethe core. To prevent the cut pieces frombrowning, soak them in lemon water.