Find a large mug or small bowl that measures about four inches in diameter.
Arrange 4 sheets fillo dough on a large cutting board. Place the mug or bowl over the dough, beginning at one corner. Use the mug or bowl as a guide to cut a small round of dough. A small serrated knife is best for cutting through the dough.
Press the small round of dough into a muffin tin to form a mini crust, and repeat until one muffin tin is filled.
Arrange 4 more sheets of fillo dough on the cutting board and repeat the process, filling a second muffin tin.
Pour 2 tablespoons olive oil into a small bowl and, using a pastry brush, brush some oil all over the inside of each crust.
Bake for about 8-11 minutes, or until crusts are crisp and golden brown.
Meanwhile, heat 1 tablespoon of oil in a large skillet over medium-high heat. Add the cubed chicken and season with a pinch of salt and pepper. Saute until chicken is golden brown, about 5-7 minutes. Transfer to a covered bowl, and set aside.
Add 3 tablespoons olive oil, along with garlic, onion, potatoes, celery, and parsnips. Season with salt and pepper. Cook until veggies begin to soften, about 7 minutes.
Reduce heat to medium. Add thyme and ground sage. Stir and combine.
Add white wine and allow it to cook and reduce down, about 2 minutes.
Add chicken broth. Also add the spinach and the cooked chicken that was set aside earlier.
Allow the broth to simmer, stirring often, until it has reduced down, about 8-11 minutes. The starch from the potatoes should thicken the broth. Season to taste with salt and pepper.
Remove fillo crusts from muffin tins. Fill each crust with heaping spoonfuls of the chicken mixture. Serve.