Prepare the grill for direct cooking over medium heat (350° to 450°F) and preheat the grill pan.
In a small bowl whisk the mustard, vinegar, salt, and pepper. Slowly drizzle and whisk in the oil until it is emulsified.
Remove and discard the tough bottom of each asparagus spear by grasping at each end and bending it gently until it snaps at its natural point of tenderness, usually about two-thirds of the way down the spear.
Spread the asparagus on a large plate. Drizzle with 2 tablespoons of the vinaigrette and turn the spears until they are evenly coated. In a medium bowl toss the tomatoes and bread cubes with 2 tablespoons of the vinaigrette.
Brush the cooking grates clean. Spread the tomatoes and bread cubes in a single layer on the grill pan and lay the asparagus on the cooking grate. Grill over direct medium heat, with the lid closed as much as possible, until the asparagus is tender, the tomatoes begin to soften, and the bread cubes are toasted, turning often. The asparagus will take 6 to 8 minutes and the tomatoes and bread cubes will take 2 to 4 minutes.
Arrange the asparagus on a platter and top with the tomatoes, croutons, feta, and chives. Serve with the remaining vinaigrette.