In a large skillet, melt butter over medium-low heat. Stir in chopped onions and allow to soften.
Add in garlic cloves and cook for 30 seconds until fragrant.
Stir in remaining ingredients except for the heavy cream and bring to a simmer.
Cook for 30 minutes. Use an immersion blender to blend until smooth.
Stir in heavy cream and serve with grilled cheese.