Preheat the oven to 425 degrees. Place the onions in a casserole deep enough so the won't touch the foil when wrapped.
Season the onions with salt and pepper. Place a pat of butter on the top of each reserving a 1/2 tablespoon of the butter for the sauce. Lay a branch of rosemary on top of each onion and then drizzle with olive oil.
Wrap the casserole tightly with foil and place into the oven for 30 minutes. Reduce the heat to 350 degrees and set the timer for another 30 minutes.
While the onions are cooking place a small sauce pan over medium high heat and add the remaining butter and the garlic. Sweat the garlic but do not let it brown. When it has softened add the cream. Bring it to a boil and then reduce the heat to low. Let it reduce by half. Add the cheese and stir to combine. Taste it and adjust the seasoning
When the timer has gone off remove the onions from the oven and top each onion with a scant tablespoon of the alfredo sauce, garnish with chives and rosemary and serve. Serve the remainder of the sauce on the side.