In a large pot, melt 2 TBS of the butter over medium high heat.
Add in the onions and cook for about 2-3 minutes.
Add in the minced garlic, potatoes, carrots, and celery. Cook for about 5 minutes until the vegetables start to get tender.
Add in the remaining butter until melted.
Add in the flour and stir it to coat the vegetables and create a roux (a thickener), cook for 1-2 minutes.
Slowly pour in the chicken broth, while stirring. Pour in the half and half the same way.
Allow the soup to come to a boil, the lower the temperature to medium low, and cook until the soup starts to thicken, about 8 minutes.
Add in the chicken, peas, corn, salt and pepper, and cook for about 4-5 minutes to heat through.