How to Make It
In a medium bowl, whisk together vinegar, mayonnaise, mustard, 2 tablespoons oil,and pepper until emulsified. Set aside.
In a large cast-iron skillet, heat 1 tablespoon oil over medium-high heat until it begins to shimmer. Cook ham until lightly golden brown (about 1 minute per side). Remove to a plate lined with paper towels. Reserve oil in skillet. Cook the tomatoes until lightly golden brown and just warmed through (about 30 seconds per side). Using paper towel, wipe out skillet and reserve it.
Heat a grill pan over high heat. Grill the bread cut side down until lightly golden brown (about 30 seconds). Turn over and grill for 20 seconds longer. Transfer bread to plates.
While bread toasts, heat reserved skillet over medium heat and add 1 tablespoon oil. Carefully crack the eggs into the pan, season with pepper, and cook until the whites are completely firm (about 2 minutes). Carefully flip eggs over and cook 30 seconds longer.
To serve, divide ham (1/2 slice per sandwich)and tomatoes among bread slices. Add frisée to reserved dressing and toss to coat. Top each sandwich with fried egg and frisée salad. Serve immediately.