In a medium saucepan, melt butter over medium-high heat.
Add onions and garlic and cook 3 to 4 minutes, stirring occasionally, until tender.
Add flour to pan,
Gradually add milk into flour mixture while stirring until mixture is smooth.
Add broth, milk, salt, pepper and nutmeg and heat thoroughly.
Add cheese to soup and cook, stirring occasionally, until cheese melts, about 5 minutes.