In a large saucepan saute together white onion and butter over medium heat. Saute onion until it becomes fragrant and translucent. Sprinkle 4 tablespoons of flour over the onions. Cook flour and onions together for about 1 minute. The mixture will become fragrant like pie dough. Slowly add about 1/4 of the half and half to the soup, stir continually. Add an additional 1/4 of the half and half and stir, the mixture will thicken. Add remaining 1/2 of half and half and stir until the soup base becomes smooth.
In a small pot at diced potatoes. Cover potatoes with just enough water to cover the potatoes. Cook the potatoes on medium-high until they become tender. Drain potatoes, and reserve for soup. Add chopped chicken breast, frozen vegetables, potatoes, and chicken base. Stir until the soup is well blended. While the soup is heating through you can cook the puff pastry. Cut the puff pastry into sizes that best fit for your bowl. I use 3-inch by 3-inch squares. Bake puff pastry until golden brown, this will take about 15 minutes.