Fill a wide, shallow pot with 2 inches of water. Add 1/2 tablespoon vinegar and bring to a gentle simmer.
Meanwhile, divide the brie between the baguette pieces and sprinkle with about 1 tablespoon of the basil. Whisk the mustard, the remaining 1 1/2 tablespoons vinegar, 1/2 teaspoon salt, and pepper to taste in a large bowl. Slowly whisk in the olive oil until smooth.
One at a time, crack each egg into a small bowl or cup, then slip into the simmering water. Poach the eggs until the whites are set but the yolks are still runny, 2 to 3 minutes. Using a slotted spoon, transfer the eggs to a paper towel-lined plate to drain briefly.
Add the mixed greens, frisee and the remaining basil to the bowl with the dressing and toss; season with salt and pepper. Divide among plates and top with the tomato and ham. Season the eggs with salt and pepper and add to the salads. Serve with the baguette pieces.
Photograph by Christopher Testani