Preheat oven to 375 degrees.

Slice off the top of the head of garlic and discard. Drizzle the head of garlic with olive oil so that it seeps down into the cloves. Wrap in foil and place on a baking sheet.

Roast for 30 minutes.

Meanwhile, add the butter to a medium skillet over medium heat. Let melt.

Once the butter has melted, add the onions to the skillet and stir to coat. Let cook for five minutes, stirring occasionally. The onions should start to turn brown. Continue cooking until onions are very soft, about 40 minutes. Stir every ten minutes. Add a couple of tablespoons of water if you notice the onions starting to stick to the pan. The water will cook off quickly.

While the onions and garlic are cooking, place the prosciutto on a baking sheet in a single layer and bake for 15 minutes. Remove from the oven and let cool. Once cooled, chop or crumble into small pieces. Set aside.

When the onions are browned and soft, reduce the heat to low. Add the cream cheese to the pan and stir constantly until it has melted.

Stir in the Grand Cru until very soft and nearly melted. Stir in the chives and milk.

Squeeze two to three cloves of the roasted garlic into the cheese mixture and add in the prosciutto. Stir well until everything comes together.

Serve immediately or transfer to a slow cooker set to warm.