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

In a mixing bowl, combine the ground turkey, egg, breadcrumbs, onion, 1 teaspoon of the Dijon mustard, thyme, salt, and pepper. Mix just until combined, then shape the mixture into a compact loaf about 8 inches long.

Unfold the thawed puff pastry on a lightly floured surface. Spread the remaining Dijon mustard down the center, leaving a border around the edges. Place the turkey loaf on top. Fold the pastry over the loaf, overlapping the edges underneath. Press the seams together, then place the wrapped loaf seam-side down on one side of the prepared baking sheet.

Toss the carrot sticks with the olive oil and arrange them in a single layer beside the pastry-wrapped loaf. Brush the top and sides of the pastry with the beaten egg.

Bake until the pastry is golden and the turkey reaches 165°F in the center, about 40 to 50 minutes. If the pastry browns before the turkey is cooked through, loosely cover it with foil. Check the carrots for tenderness and remove them if they finish first.

Let the Wellington rest for 10 minutes before slicing. Serve with the roasted carrots.