Heat a medium saute pan on medium heat and add the butter. Once the butter has melted, add the shallots and cook until translucent (do not burn) for about 4 minutes.
Add the garlic and cook for 1 - 2 minutes (do not burn) Add the artichoke hearts and cook until heated through. About 4 minutes. Season with salt and pepper. Set aside to cool completely.
Preheat the oven to 350 degrees. Place the cream cheese, sour cream and giardiniera in a food processor and blend until mixed thoroughly. Add the artichoke heart mixture and briefly buzz until just mixed. Do not incorporate the artichoke hearts too much; they should be medium in size.
To plate, place ¼ cup of the artichoke dip in a small oven-safe ramekin and bake for 7 - 10 minutes or until the top is bubbly. Remove from oven and garnish with 1 tablespoon of the giardiniera. Meanwhile, brush ciabatta with oil, salt, and pepper. Grill or toast. Place bread on the side of the dip, and garnish both the bread and dip with chives.