Season the pork with salt and pepper. In a small enameled cast-iron casserole, melt 2 tablespoons of the butter. Add the pork and brown well over moderately high heat, 10 minutes; transfer to a plate. Pour off the fat from the casserole. Add the wine and boil over high heat, scraping up the browned bits, until reduced by half, 3 minutes. Add the broth and bring to a boil. Add the garlic, bay leaf, thyme sprig, yellow onion and the pork. Cover and simmer over very low heat, turning once, until an instant-read thermometer inserted in the center registers 160°, about 1 hour.
Meanwhile, in a medium saucepan of water, boil the pearl onions until almost tender, 5 minutes; drain and peel. In a bowl, blend the 2 tablespoons of softened butter with the flour to form a paste.
Transfer the pork to a plate. Strain the cooking liquid and return to the casserole; boil until reduced to 2 cups, 4 minutes. Whisk 1/2 cup of the cooking liquid into the flour paste until smooth, then whisk the mixture into the cooking liquid. Simmer over moderately high heat, whisking, until thickened. Simmer over low heat, stirring, until no floury taste remains, 5 minutes. Stir in the chopped thyme and season with salt and pepper. Return the pork and its juices to the casserole and add the pearl onions. Cover and bring just to a simmer, turning the pork a few times in the sauce to heat it up.
In a skillet, melt the remaining 1 tablespoon of butter. Add the grapes and cook over moderately high heat, shaking the skillet, until the skins start to burst. Thickly slice the pork and transfer to plates. Spoon the sauce, pearl onions and grapes on top; serve.
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