Preheat oven to 400 degrees. In a large saucepan, sauté onion in olive oil. Then add peas and carrots, chicken/turkey, potatoes, milk, ½ teaspoon thyme, and soup. Bring to a boil over medium-high heat, stirring occasionally. Divide mixture evenly amongst 4 ungreased 10-ounce ramekins.
Unroll the dough and separate into 4 triangles. Place 1 dough triangle over each ramekin.
In a small bowl, mix egg and water. Brush the mixture over the dough, then sprinkle 1/8 teaspoon of thyme over dough.
Bake 11-13 minutes, or until crusts are golden brown.