Heat the oven to 400 degrees F.
In a small saucepot over medium heat add the oil, rosemary, thyme sprigs, garlic, and a pinch of salt. Heat until the garlic begins to brown and thyme is crisp. Strain the oil and remove the thyme to a paper towel-lined plate. Discard the rosemary and garlic, but reserve the oil.
Brush one side of each piece of bread with the oil and place them oiled-side up on a wire rack fitted inside a baking sheet with sides. On another wire rack place the strips of speck ham and brush the top of each with maple syrup. Bake in the oven until both the toast and ham are golden and crisp, about 10 minutes.
Meanwhile make the eggs. In a nonstick saute pan over medium-high heat, add a few tablespoons of the reserved olive oil. Crack each egg over the pan and allow to fry until most of the whites are cooked, about 4 minutes. Sprinkle with salt and a grind or two of pepper, then lower the heat and cover until the top of the eggs are cooked, but the yolks are not, about 2 minutes more.
To assemble the sandwiches: Spread a tablespoon of grape jelly on the oiled side of each piece of bread. Top with a few strips of folded over ham, an egg and a few sprigs of the reserved fried thyme. Garnish with the shredded Parmesan cheese.
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