Preheat the oven to 400°F (200°C) and line two baking sheets with parchment paper.
Toss the carrots with olive oil, honey, salt, and pepper on the first baking sheet and roast for 15 minutes until slightly softened.
Combine ricotta, basil, parsley, chives, garlic, lemon juice, and lemon zest in a food processor and pulse until smooth and bright green.
Place the puff pastry on the second baking sheet and lightly score a 1-inch border around the edges using a sharp knife.
Spread the green goddess ricotta mixture evenly within the scored border of the pastry.
Arrange the pre-roasted carrots in a single layer over the ricotta base.
Brush the pastry border with the beaten egg wash to ensure a golden finish.
Bake for 20 to 25 minutes until the pastry is puffed and golden brown.
Allow the tart to cool for 10 minutes before slicing and serving.