Preheat your oven to 390°F (200°C).
Make 6 slices of goat cheese and keep aside.
In a bowl, combine heavy cream and grated Gruyere. Add the minced shallot, season to taste, and mix.
Coat a first bread slice with this mixture, then place a half slice of ham on top, then a dollop of the cream preparation in the center and top with the last slice of bread.
Spread the remaining shallot cream on top of the bread. Place a slice of goat cheese on top and sprinkle with oregano. Repeat the same process for the other sandwiches, and arrange them on a baking sheet lined with parchment paper.
Bake in the oven at 390°F (200°C) until browned on top, count about 15/20 minutes. A the end of cooking, you can turn on the broiler and broil for 2 to 3 minutes or until the topping is bubbly and lightly browned. Serve hot with a green salad.