Ladle 1 tsp. of olive oil into a heated, nonstick egg pan. Break an egg into the pan. Cook the egg on one side for sunny-side up, or cook to desired doneness.
Brush the insides of the top and bottom half of the bun with 2 tsp. of olive oil. Place on a heated flat griddle, oiled side down. Grill until golden brown. Spread 1½ oz. of tomato jam on the bottom half of the bun. Place on a warmed serving plate.
Spray a heated flat griddle with pan spray. Place 1½ oz. of spinach on the griddle. Season to taste with salt and pepper. As soon as the spinach begins to wilt, place on top of the tomato jam.
Place 2 oz. of turkey on the griddle. Grill until just warmed through. Place on top of the spinach. Place 2 slices of yellow cheddar on top of the turkey. Place under a heated salamander to melt the cheese. Place the egg on top of the cheese.
Arrange the top of the bun next to the sandwich, grilled side up. Place a 2 oz. ramekin of honey mustard on the plate next to the sandwich.