Preheat the oven to 200° C/ 390° F, on convection mode.
Wash the potatoes thoroughly to remove any dirt (without peeling them).
Heat a pot with plenty of salted water and boil the potatoes for 15 minutes until they start to soften.
Remove the potatoes from the pot and let them cool completely.
Place the potatoes on a cutting board, placing 2 wooden spoons underneath the potatoes to prevent cutting through the bottom. Using a sharp knife, make slices into the potatoes without cutting all the way through.
Place the potatoes in a baking dish, and insert a piece of ham into each slit.
In a bowl, mix the melted butter, thyme, rosemary, salt, and pepper, and brush this mixture over the potatoes.
Top with the grated gruyere cheese and bake for about 20 minutes, or until the potatoes are golden brown.
Once the potatoes are done, serve them garnished with arugula and cherry tomatoes.