Remove the puff pastry from the freezer to thaw at room temp. Preheat the oven to 400 degrees F. Grease six ramekins (see notes below about sizing) and place on a baking sheet.
In a large Dutch oven or pot over medium heat, heat one tablespoon of butter. Add the onion, garlic, rosemary, thyme, salt, and pepper. Cook for a few minutes until the onion starts to soften. Add the rest of the butter, let it cook for a minute or two until melted, then stir in the flour until the veggies are coated.
Pour the milk into the pot, and whisk until the flour has dissolved. You will start to feel the mixture thicken as your stir. Pour in the veggie broth, and add the diced potatoes and frozen veggies. Simmer over medium-low heat for 10 minutes (there should be a very gentle boil going), stirring frequently, until the mixture is thickened like a pot pie filling and potatoes begin to soften. Note: the potatoes will not be fork-tender; they finish cooking in the oven. Taste and adjust seasonings as desired.
Ladle the filling into the greased ramekins, being careful not to overfill them. Slice the puff pastry into six squares, and make a few slits in the top of each pastry for steam to escape. Place a square on top of each ramekin, and carefully fold it around the edges. Depending on the size of your ramekins, you may need to cut an extra slice of puff pastry and combine it with the square to fully cover the ramekin. If your puff pastry did not thaw completely, place it on the ramekins and let it sit for a few minutes. The steam from the filling will help soften it and make it easier to bend.
Carefully transfer the baking sheet with the pot pies to the oven. Cook for 20 to 25 minutes until the puff pastry is golden brown. Remove and serve warm!