Make the pesto: Remove and discard the kale stems.  Bring a pot of salted water to a boil and blanch kale leaves 30 seconds. Drain leaves and place immediately in an ice water bath.  Squeeze the kale to remove any excess water and pat the leaves dry with paper towels. Place the kale, hazelnuts, parmesan, garlic, and lemon zest in a food processor work bowl and pulse about 15 times, until the mixture is well combined.  With the processor running slowly drizzle in the oil to make a smooth paste.  Season to taste with salt and pepper.

Make the aioli:  In a mini food processor bowl, pulse the tomatoes and garlic until finely chopped. Add the mayonnaise and pulse until well blended.

Heat the butter and sliced garlic in a small saucepan over low heat until the butter is melted.  Remove from heat and let rest at least 5minutes.  Remove garlic and discard or reserve for another use.  Reserve melted garlic butter.

Heat a large non-stick skillet over medium-high heat.  Using a 2 – 2 ½-inch cookie cutter, cut a circle from the center of 2 slices of bread and discard circle or reserve for another use. Spread the pesto on one side of the other two slices.  Heat half the reserved garlic butter in the skillet and place the two slices of bread with holes in the skillet.  Crack an egg into each hole and cook until the egg begins to set.  Flip the bread over and quickly spread with tomato aioli. Place ½ c. shredded cheese, half the turkey, half the ham, and an additional ½ c. cheese on each slice. Top with remaining slices of bread, pesto-side down. 

Add remaining garlic butter to the skillet and flip sandwiches so that the egg side is up.  Cover skillet and cook until the cheese is melted and the bottoms of the sandwiches are browned, about 3 minutes.  Serve while the egg is still hot and slightly runny.