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In a large soup pot or Dutch oven melt butter over medium-high heat. Add onion, celery and carrot and sauté for 3 to 4 minutes; until veggies start to soften.
Add garlic and cook for another 30 seconds.
Add flour, stir well and cook for another 30 seconds.
Add cooked chicken, potatoes, broth, milk and thyme and bring everything to simmer; be sure not to bring it to a boil as you do not want to scald the milk. Reduce heat to medium-low and simmer for 15 minutes or until soup is thickened and potatoes are cooked through.
In the meantime, preheat oven to 400°F. Using a small cookie cutter or drinking glass to cut store-bought pie crust dough into discs.
Transfer the pie crust crackers to a baking sheet and brush with egg wash. Sprinkle with onion powder, thyme, salt and pepper.
After the soup has simmered for 15 minutes, remove the stem from the thyme and add frozen peas and corn and cook for another 2 to 3 minutes.
Season with salt and pepper to taste and serve with crackers.