Melt 1 tablespoon of butter in a large pot over medium high heat.
Add in onions and cook until softened.
Add garlic and cook for another minute.
Add the broth.
Add thyme and poultry seasoning and bring to a boil.
Add potatoes and reduce to a simmer and cook for about 10 minutes.
In another pan, melt remaining butter over medium heat.
Add flour to the melted butter and stir while it cooks for a couple of minutes.
Keep stirring while adding the milk to the roux until mixture is well blended.
Add this sauce to the larger pot and stir until blended.
Slowly add in the half and half while stirring to mix well.
Add green beans, corn, peas and carrots. Stir to mix.
Add chicken, stir and cook over low heat until everything is heated through (about 15 minutes).
Salt and pepper to taste.