Make the crust: Place a rack in the center of your oven and preheat to 375°F (for crescent rolls) or 425°F (for regular pizza dough). Line a large rimmed baking sheet with parchment paper.: Place a rack in the center of your oven and preheat to 375°F (for crescent rolls) or 425°F (for regular pizza dough). Line a large rimmed baking sheet with parchment paper. : As the oven heats you will smell a dry warmth building, signaling the environment needed for a crisp crust. Preheating to the correct temperature ensures even browning and proper rise, so the crust firms quickly instead of becoming greasy. The parchment creates a nonstick surface and keeps cleanup simple. A frequent error is skipping preheat, which leads to a pale, underbaked base that will not crisp properly.
If using crescent roll dough, unroll the tubes onto the parchment and line up the triangles so you form a single flat crust. Pinch the seams together. If using pizza dough, roll it out on a lightly floured work surface into an approximate 11×14-inch rectangle, working from the center outward. Gently transfer it to the baking sheet, then poke all over with the tines of a fork. (You can also roll the dough onto a sheet of parchment, then lift it with the paper onto the baking sheet.): You'll feel the dough yield under your fingertips as you shape it, and the small fork holes keep air pockets from forming that would create uneven bubbles. Pinching seams on crescent dough prevents separation and uneven baking, while poking pizza dough encourages a flat, even crust. One slip is overworking the dough, which tightens the gluten and makes a dense crust; handle it gently.
Bake until the crust is light golden brown, about 12 to 15 minutes (the time is the same for both crescent dough and pizza dough). Let cool for at least 30 minutes.: As it bakes you will notice the edges begin to take on a warm, golden hue and a faint toasty aroma. Cooling is crucial because a hot crust will melt the topping and make it slippery, so letting it rest ensures the cream cheese spreads cleanly and adheres. Cutting too soon often leads to a soggy, messy slice, so patience pays off here.
While the crust cools, make the cream cheese topping: In a medium bowl, stir together the cream cheese, Greek yogurt, garlic powder, onion powder, dill weed, salt, and cayenne (if the cream cheese is soft, you don’t need a mixer).: In a medium bowl, stir together the cream cheese, Greek yogurt, garlic powder, onion powder, dill weed, salt, and cayenne (if the cream cheese is soft, you don’t need a mixer). : The aroma of dried herbs and spices will bloom as you stir, and the texture should become silky and uniform. Mixing by hand preserves a slightly rustic texture that helps the vegetables cling. If the mixture is too cold it will be lumpy and hard to spread, so let the cream cheese sit until it is soft enough to stir smoothly.
To assemble, spread the cream cheese mixture over the crust like 'sauce,' leaving a thin border of crust all the way around. Sprinkle with the broccoli, lightly pressing it to adhere to the cream cheese. Add half of the cheese and the bell pepper, then lightly press again. Finish with the carrots, remaining cheese, and green onions. If desired, crack black pepper over the top.: The tactile act of spreading creates an even bed for the vegetables, and pressing the chopped broccoli and other toppings lightly ensures they stay put when slicing. Layering the cheddar cheese in two stages helps it meld the vegetables to the base without overwhelming them, and finishing with green onions adds color and a fresh bite. Avoid piling too high in one area, which can cause uneven slices and slipping toppings.
Slice and enjoy immediately, or for best results, cover and chill for at least 1 hour or up to 8 hours. Slice and enjoy!: Chilling firms the topping and allows flavors to marry, creating cleaner slices and a more cohesive bite. When you slice after chilling you will notice cleaner edges and a compact texture, making it ideal for parties. One common mistake is leaving it out too long on a warm day, which can soften the crust and make the topping less pleasant to handle.