In a large cast-iron or a non-stick pot, heat three tablespoons olive oil over medium-high heat. Add the leeks, mushrooms, carrots, and garlic. Cook for 5 minutes until the leeks and carrots soften.
Add the mustard, flour, stock, sour cream, and potatoes. Cook for 10 minutes then stir in peas, corn, and thyme. Simmer for 15 minutes until the sauce thickens. Season with salt and pepper to taste.
Divide the vegetable mixture between six 12 ounce ramekins or pie dishes. Preheat oven to 350 degrees Fahrenheit.
Lay out a sheet of fillo on a clean surface with the longer side facing you and brush generously with olive oil. Roughly scrunch the fillo together to form a "log" and gently coil it up to form a rosette. Top each pie with three of the fillo rosettes.
Place the pies on a cookie sheet to catch any dripping. Brush the rosettes with remaining oil and bake for 20-30 minutes or until the fillo is golden brown. Cool for 5 minutes before serving.
Substitute potatoes with chicken for a non-vegetarian version. Cook chicken before adding the vegetables.
Use butter instead of olive oil for a richer flavor.
Instead of making rosettes, coil fillo "logs" around the ramekin for one large rose. Coil together with blanched carrot ribbons for added color.