Move oven rack to middle position and preheat to 350 degrees F. Line baking sheet with parchment or silicone baking mat.
Roll out Crescent Rolls onto the prepared baking sheet. Pinch seams together to create a rectangular piece of dough and bake until golden brown, about 7-8 minutes. Move baking sheet to wire rack to cool completely, about 40 minutes. Once cool move crust to a large cutting board.
Once the crust is cooled add cream cheese, sour cream, chives, and dill to a medium bowl. Stir mixture until combined and no lumps remain. Spread the mixture, using a small rubber spatula or offset spatula, evenly over crust. Distribute veggies over cream cheese mixture and press veggies down lightly. Slice pizza into 24 pieces and serve immediately.