Preheat oven to 350 degrees. Bring a large pot of water to boil and cook the macaroni according to package directions. Drain and set aside.
In a sauce pot, heat the olive oil over medium heat. Add the shallots and garlic and cook until shallots are translucent, about 3 minutes. Add the half-and-half and cream and bring to a simmer.
Meanwhile, in a separate saute pan, melt the butter. Add the flour and whisk over low heat until fully incorporated, about 1 to 1 1/2 minutes, to make a blond roux. Whisk the roux into the simmering cream. Add a little of the cream to the beaten egg, then stir the egg into the cream mixture.
Once the egg is fully cooked into the mixture, about 1 minute, remove from heat, add the salt and fold in 2 cups grated cheese. Fold in the macaroni along with an additional 2 cups cheese and the chives. Transfer to a buttered 9-inch- square baking dish. Top with the remaining 1 cup cheese.
Cover with aluminum foil and bake for 15 minutes. Pull off the foil and bake, uncovered, for an additional 5 minutes.