Peel out layer from garlic and slice 1/4 inch off the top, exposing the cloves.
Combine sliced onion and garlic in a small baking dish and drizzle with olive oil.
Place sliced peppers cut side down on a foil lined baking sheet. Place onion/garlic mixture and peppers into oven and bake for 20-25 minutes until skin on peppers is browned and bubbly and garlic is soft.
Wrap peppers in foil and allow to sit for about 20 minutes. When cool enough to handle remove the skins from the peppers. Discard skins. Press garlic
Combine onion mixture, sweet peppers, parsley, basil, jalapeno, salt, pepper in a blender or food processor. Blend until smooth. Add in chicken broth and sugar.
Heat on stove and add in half and half.
Cool and refrigerate. Flavors will combine as it chills. Can be served immediately if desired but I like the flavor better the next day.