1. Place the meat in a large heavy pot and add the white onion, 5 of the garlic cloves, the bay leaves, and 1 tablespoon salt. Cover by at least 1 inch with water and bring to a boil over high heat. Reduce to the lowest possible heat, cover, and cook for 1 hour, or until the meat is so soft that it shreds easily when pulled apart with a fork.
2. Meanwhile, combine the vinegar, oils, the remaining 2 garlic cloves, 1 tablespoon salt, pepper, and sugar in a blender and puree until com-pletely smooth. Pour into a jar, add the red onion, and shake well; set the vinaigrette aside.
3. Bring a medium saucepan of salted water to a boil. Add the potatoes, then reduce the heat to medium and, keeping the water at a steady, gentle boil, cook just until they are tender all the way through, about 20 minutes. Remove the potatoes with a slotted spoon and place in a bowl. (Keep the water in the saucepan at a gentle boil.) As soon as the potatoes are cool enough to handle, cut them in half, return them to the bowl, and toss with 1⁄2 cup of the vinaigrette (but not the red onion) so they will absorb the dressing while still warm.
4. Add the carrots to the boiling water and cook until barely cooked, less than 1 minute. Remove with the slotted spoon and place in another bowl. Add the green
beans to the boiling water and cook until crisp-tender, about 3 minutes, then remove with the slotted spoon and add to the carrots. Add the peas to the boiling water and cook for 20 to 30 seconds, until barely cooked through; remove with the slotted spoon and add to the green beans and carrots. Add the radishes to the bowl along with 1⁄2 cup of the vinaigrette and toss together.
5. When the meat is done, drain it and discard the cooking liquid. Once the meat is cool enough to handle, shred it and place in a bowl.
6. Shake the vinaigrette again and add 1⁄2 cup to the meat, along with the macerated onions, and toss together.
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