For the Dough:

1. Combine flour and salt in a large bowl. Cut in the butter with a pastry cutter until the butter is broken into pea-sized pieces and evenly distributed throughout the flour.
2. Cut in the yogurt and water until just incorporated. The dough should not be fully mixed. 
3. Add the herbs and work them into the dough with a sturdy spoon or your hands to form a cohesive dough without overmixing.
4. Form the dough into a disc, lightly sprinkle with flour, and tightly cover with plastic wrap. Place in the refrigerator and chill for at least 30 minutes or up to 1 hour. Prepare the carrots and yogurt as the dough chills.

For the Carrots:

1. Preheat the oven to 375°F. In a large bowl, whisk together the olive oil, honey, and cumin.
2. Prep the carrots by peeling the skins and chopping off the tops and bottoms. Cut the carrots in half lengthwise and place in the large bowl. Depending on the length, you may need to cut larger carrots in half horizontally as well. Combine with the oil mixture until the carrots are completely coated.
3. Transfer the carrots to a baking sheet lined with aluminum foil or a silicone mat, arranging them in a single layer. Sprinkle with the salt and pepper. Roast for 20-25 minutes, turning the sheet halfway through, until the carrots are crisp-tender and starting to brown around the edges and tips.
4. Remove from the oven and let cool completely, about 20 minutes.

For the Yogurt Spread:

In a small bowl, whisk together the yogurt, cumin, basil, salt, and pepper. Place the bowl in the fridge until ready to use.

To Assemble and Bake:

1. Raise the temperature of the oven to 400°F. 
2. Remove the chilled disc from the fridge and place on a lightly floured surface. Let sit at room temperature for 5-10 minutes. Using a rolling pin, roll out the dough into a circle about 12 inches in diameter. Carefully transfer the dough to a baking sheet lined with parchment paper or a silicone mat.
3. Spread half of the yogurt sauce in the center of the dough, leaving a border of about 2 inches around the edges. Place the remaining sauce in the refrigerator for serving. 
4. Top the crostata with the roasted carrots, shingling them as needed.
5. Fold the edges of the dough towards the middle, crimping the dough to create pleats. Briefly whisk the egg and tablespoon water so they are lightly beaten together and lightly brush the crust with the egg wash.
6. Bake 35-40 minutes or until the crust is golden, turning the baking sheet halfway through baking. Remove from the oven. Let cool slightly, about 10 minutes. Serve!