Step 1
Preheat oven to 425°. Arrange 4 large shallots, peeled, quartered lengthwise, and 2 lb. medium carrots, scrubbed, trimmed, on a rimmed baking sheet. Drizzle with extra-virgin olive oil, season with kosher salt, and toss to coat. Roast until carrots are mostly tender, 27–32 minutes. Transfer half of carrots to a cutting board and coarsely chop; set remaining whole carrots on baking sheet aside.
Step 2
Meanwhile, toast 1 cup raw walnuts on another rimmed baking sheet in a single layer, tossing halfway through, until golden brown, 8–10 minutes. Transfer to a food processor; reserve baking sheet. Very finely chop nuts; transfer to a large bowl.
Step 3
Transfer chopped carrots and roasted shallots to food processor; process until a rough paste forms. Transfer to bowl with walnuts. Add 4 oz. goat cheese, room temperature, 3 oz. Gruyère, coarsely grated (about ¾ cup), ¼ cup finely chopped parsley, 1 Tbsp. curry powder, and 1 Tbsp. Diamond Crystal or 1¾ tsp. Morton kosher salt; season with freshly ground pepper and mix well.
Step 4
Stir 2 Tbsp. Dijon mustard, 1 Tbsp. honey, and remaining ½ tsp. curry powder in a small bowl to combine. Drizzle over reserved whole carrots on baking sheet and toss to coat.
Step 5
Roll out 1 sheet frozen puff pastry (one 14-oz. package or half of a 17.3-oz. package), thawed, on a lightly floured surface to a 16×13″ rectangle. Arrange so a long side is facing you. Spread walnut mixture over pastry, creating a rectangle as long as the carrots and leaving a 1″ border across top and bottom of pastry. Pile glazed carrots on top of walnut mixture toward bottom of pastry (point skinny ends in opposite directions as needed to create even stacking). Working with the edge closest to you, roll pastry up and over carrots, then continue to roll up pastry all the way to the other side; press and pinch dough to seal. Turn pastry seam side down and transfer to reserved baking sheet; twist ends to seal, trim off any excess pastry, and tuck ends underneath Wellington to make sure filling is completely encased. Chill until pastry is firm, at least 30 minutes.
Step 6
Reheat oven to 450° if needed. Brush top and sides of Wellington with 1 large egg, beaten to blend. Using a small knife, cut slits no longer than 1″ in a decorative pattern across entire surface of dough. Bake Wellington until pastry is golden brown, 30–35 minutes. Let cool slightly on baking sheet.
Step 7
Meanwhile, process ¾ cup plain whole-milk yogurt, ¼ cup fresh lemon juice, and remaining ¼ cup finely chopped parsley in clean food processor to combine. Season yogurt sauce with salt and transfer to a small bowl.
Step 8
Using 2 metal spatulas if needed, transfer Wellington to a platter. Serve with yogurt sauce alongside.