Preheat the oven: Preheat your oven to 400°F (200°C). Line a large baking sheet with parchment paper for easy cleanup.
Roast the carrots: Arrange peeled and halved carrots on a parchment lined baking sheet, with ends trimmed off. Drizzle with olive oil and season with kosher salt and freshly ground black pepper. Turn the carrots cut-side down, spreading them out side by side across the pan. Roast for 15 minutes, until just tender and starting to caramelize. Remove from the oven and set aside. (oven remains on)
Make the herbed goat cheese: In a food processor, combine the crumbled goat cheese, dill, parsley, chives, garlic, lemon zest, lemon juice, salt, and pepper. Blend until smooth and creamy, scraping down the sides as needed. Tip for the spread: Pipe the spread into a quart sized zip bag. When it’s time to assemble the tarts, snip a 1” triangle off the corner edge and pipe onto the unbaked puff pastry.
Roll out the puff pastry: On a lightly floured surface, cut and roll the thawed puff pastry into four 3.5 x 10-inch (9 x 25 cm) rectangles. Place them evenly spaced on a parchment-lined baking sheet. Use a fork to prick the pastry all over — this helps prevent excess puffing while baking.
Score the pastry sheets: Using a straight edge or knife, score a ¾-inch (2 cm) border around each rectangle to create a guide for the filling.
Brush with egg wash: In a small bowl, whisk 1 large egg (50 g) with a fork. Brush the exposed ¾-inch (2 cm) edges of each pastry with the egg wash — this will give the crust a golden, glossy finish when baked.
Assemble the tarts: Spread or pipe on the herbed goat cheese evenly over the centers of each pastry rectangle, staying within the scored lines. Arrange the roasted carrots cut-side down over the cheese, using 2 carrot halves per tart. Place them opposite each other, fat end to skinny end, creating a balanced shape.
Bake the tarts: Bake for 20 to 25 minutes, or until the pastry is deeply golden and crisp.
Add toppings and serve: Top each tart with a handful of arugula or microgreens (about ¼ cup - 6 g per tart). Drizzle lightly with hot honey (about ½ tablespoon each - 7 ml total).
Slice and enjoy: Transfer the tarts to a cutting board. Slice each tart in half, yielding 8 servings total. Serve warm or at room temperature.