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Bring 2 quarts water and ¼ cup salt to a boil in a large pot over high. Prepare a large bowl of ice and water. Add onions to boiling water; cook until slightly softened, about 3 minutes. Transfer onions to ice bath using a slotted spoon. Add carrots to boiling water; cook until almost crisp-tender, 5 to 7 minutes. Drain carrots, and add to ice bath. Let carrots and onions stand until cool, about 2 minutes. Drain and pat dry.
Trim off root ends of onions. Squeeze onions to remove from skins; discard skins. Set onions aside.
Melt butter in a large skillet over medium; cook, whisking often, until butter is browned and smells nutty, 3 to 5 minutes. Whisk in honey, vinegar, pepper, and remaining ½ teaspoon salt. Add carrots and onions, and increase heat to medium-high; cook, tossing often, until carrots are crisp-tender and sauce is thickened and glossy, about 5 minutes. Transfer to a serving platter, and sprinkle with tarragon.