Trim root end of leeks, leaving them as intact as possible so they don’t break apart while cooking. Cut in half lengthwise. Don’t throw away the tough outer leaves. Keep in the freezer and use with other scraps to make stock.
Preheat oven to 325 degrees and adjust rack to middle position. Heat 1 tablespoon olive oil in a large ovenproof skillet over medium-high heat until shimmering. Add leeks in a single layer cut side down. Cook, shaking occasionally until slightly golden. Flip leeks so they are cut side up and sprinkle with sea salt and pepper. Add wine and broth. Cover with a lid or aluminum foil and bake in oven for 20 minutes. Remove cover and continue to cook until leeks are completely tender and translucent and most of the liquid has evaporated, about 10 minutes longer.
Meanwhile whisk shallot, garlic, lemon juice, sugar and mustards in a small bowl. Gradually add ¼ cup oil and 1 tablespoon water, continuing to whisk. Season vinaigrette with sea salt and pepper.
Remove leeks from oven, drizzle with vinaigrette, sprinkle with lemon zest and serve.