Preheat the oven to 350F degrees.
In a large mixing bowl, mix together all the ingredients for the dough. Once a uniform dough has formed, transfer it onto a floured surface and kneed together for 5 minutes. Return the dough to the bowl. Cover with a towel and set aside for 10 minutes.
Meanwhile, peel and slice thinly the sweet potato, carrot, and beet.
Next, roll the dough into a circle ¼" thick. Note: Be careful not to roll too thin because you want a stable dough that will hold the filling. Transfer the dough to the prepared sheet tray with parchment paper.
Layer the sliced vegetables evenly in the middle of the dough, leaving a 1 ½-inch border. Finally, fold the edges of the dough up and over top of the vegetables. Sprinkle the vegan feta cheese over the vegetables and brush olive oil over the entire top. Finish with fresh rosemary and flaky sea salt.
Bake in the preheated oven for 30-35 minutes, until the edges are golden brown. Once out of the oven, sprinkle with more vegan cheese and fresh rosemary.