Bring a large pot of salted water to a boil. Add the potatoes and cook until tender, about 15 minutes, adding the red onions during the last 4 minutes of cooking. Remove with a slotted spoon; blot dry with paper towels.
Prepare a large bowl of ice water. Return the pot of water to a boil; add the Brussels sprouts and cook until tender, 6 to 7 minutes. Drain and immediately transfer to the ice water. Stir a few times until cooled, then drain the Brussels sprouts; blot dry with paper towels. (The vegetables can be prepared to this point up to 2 hours ahead; cover and refrigerate.)
Melt the butter in a large skillet over medium heat. Add the thyme, vinegar and honey and bring to a simmer. Add the vegetables and toss until glazed and heated through, about 3 minutes, adding a few tablespoons of water if necessary. Season with salt and pepper and toss with the parsley.