Preheat oven to 425 degrees. Cook shallot in oil in a large pot over
medium heat until soft, about 4 minutes. Add carrot, parsnip,
and potato. Cook until soft, about 10 minutes. Add wine; simmer
until reduced by half, about 2 minutes. Add stock; bring to
a boil. Add chicken and thyme. Cook for 2 minutes. Season
with salt and pepper. Add cornstarch mixture and cream. Bring
to a simmer; cook until thick, about 5 minutes.
Divide mixture among four 6-ounce ramekins; top with
pastry. Brush with egg. Cut a hole into each to vent. Bake on
a baking sheet until golden, 12 to 14 minutes.