Whisk the vinegar, mustard and a pinch each of salt and pepper in a large bowl. Gradually whisk in 1 tablespoon olive oil until smooth.
Heat the remaining 1 tablespoon olive oil in a large nonstick skillet over medium-high heat. Add the ham and cook until browned, 2 to 3 minutes per side. Remove each piece to a plate. Reduce the heat to medium low. Working in batches, crack the eggs into the skillet and cook, without flipping, until the whites are set but the yolks are still runny, 4 to 5 minutes. Season with salt and pepper. Divide among the plates.
Add the bell pepper, mesclun greens and chives to the bowl with the vinaigrette and toss to coat. Season with salt and pepper. Add the salad to the plates. Serve with the baguette.
Photograph by Justin Walker