Preheat oven to 425 degrees F. Heat a large pot over medium heat and add olive oil and butter.
Stir in onions, carrots, celery, leeks, salt and pepper, tossing to coat, then let cook until soft, about 5 minutes. Stir in garlic and cook for 30 seconds, then stir in flour.
Stir well to distribute the flour throughout the vegetables and coat them, then cook for about 3-5 minutes, stirring to create somewhat of a roux and thickening agent.
Most of the flour will stick to the vegetables, but you do want it to turn a slightly golden color and smell a bit nutty. (ha... that sounds interesting.)
At this point, use a biscuit cutter (or even a knife) and cut 12 "biscuits" out of your thawed puff pastry sheet.
Place them on a baking sheet (brushing with some beaten egg if desired) and bake for 10-12 minutes, or until golden brown.
Add in potatoes, chicken stock and half and half to the soup, stirring and allowing the mixture to come to a bubble.
Reduce heat to medium low, add in chicken, peas and corn and cover, simmering for 10-15 minutes.
Taste and season with more salt and pepper if needed. Serve with puff pastry on top!