For vinaigrette, in a small bowl whisk together vinegar and mustard until smooth. Add shallots, sugar, olive oil, salt, and pepper. Whisk to combine. Set aside.
Season steaks lightly with additional salt and pepper. For a charcoal grill, grill steaks on the rack of an uncovered grill directly over medium coals for 11 to 15 minutes for medium-rare (145 degrees F) or 14 to 18 minutes for medium (160 degrees F), turning once. Add the hoagie buns to the grill rack, cut side down; grill about 1 minute or until toasted.
Slice steaks into strips. On bottom half of grilled buns place spinach, steak, and cheese. Drizzle with vinaigrette. Garnish with red pepper strips. Makes 6 servings.
Roasted Red Pepper Strips
Quarter a medium red sweet pepper; remove stems, seeds, and membranes. Place pepper quarters, skin side down, on grill rack directly over medium coals. Grill for 10 to 12 minutes or until skin is charred. Wrap in foil and let stand 5 minutes while slicing steak. Use a sharp knife to loosen the edges of the skins from the pepper quarters; gently and slowly pull the skin from the pepper quarters. Discard skin. Cut pepper quarters into strips or 3/4-inch pieces.