Heat the oven to 400°F. Line a rimmed baking sheet with parchment paper.

Warm the olive oil in a small skillet over medium heat. Add the chopped onion and cook for 4 to 5 minutes, stirring occasionally, until softened. Set it aside to cool.

In a large bowl, combine the ground turkey, egg, milk, breadcrumbs, cooled onion, Dijon mustard, thyme, salt, and black pepper. Mix gently until combined, taking care not to pack the mixture tightly.

Shape the turkey mixture into a compact loaf on the prepared baking sheet. Bake for 25 minutes, until the outside is set but the center is not yet fully cooked. Let it cool for 10 minutes so it is easier to wrap.

Unfold the thawed puff pastry on a lightly floured surface. Roll it out slightly, if needed, so it is large enough to wrap around the loaf. Place the cooled meatloaf in the center and fold the pastry over it. Pinch the seams together and place the loaf seam-side down on the baking sheet.

Brush the pastry all over with the beaten egg. Bake for 25 to 30 minutes, until the pastry is deep golden and the turkey reaches 165°F in the center.

Rest the Wellington for 10 minutes before slicing. Use a sharp knife to cut through the flaky pastry without pressing down on the tender filling.