In a medium bowl, combine the active dry yeast, 1 tsp of the sugar and ¾ cup warm water (about 100 degrees). Let sit until frothy, about 10 minutes. \nMeanwhile, add the flour, remaining 2 tsp sugar and salt to a large bowl and whisk to combine.\nOnce the yeast is frothy, whisk in the yogurt and olive oil. Add the yeast\/yogurt mixture to the dry ingredients and combine using a fork. Once the dough has come together, coat your hands with flour and knead the dough to form a soft, sticky ball. As soon as the ball comes together, stop kneading.\nTransfer the ball to a lightly oiled bowl and cover with a damp kitchen towel or plastic wrap. Let sit in a warm place for 1 to 1 ½ hours until doubled in size. Meanwhile, prepare the toppings: Using a mandoline or vegetable peeler, thinly slice the squash into long ribbons. Place in a mixing bowl.\nIn a small bowl, whisk together the lemon juice, olive oil, ¼ cup This Little Goat went to Korea and a pinch of kosher salt. Pour half of the dressing over the squash (reserving the other half) and toss to combine. \nIn a small pot, melt 2 Tbsp butter and whisk in remaining ¼ cup Korea sauce. Set aside. \nDivide dough into 4 equal-sized portions. Using a rolling pin, roll each ball of dough into a large circle, about ⅛-inch thick. \nHeat a large cast-iron or non-stick skillet over medium heat. Place the dough in the preheated skillet and cook until the top is bubbling and bottom is deep golden brown, about 3 minutes. Flip over and brush with the Korea butter mixture. Top with a quarter of the marinated squash and feta. Cover and continue cooking until the bottom has browned and squash has begun to wilt, about 2-3 minutes more. \nRemove from heat and transfer to a serving plate or cutting board. Toss arugula with reserved Korea vinaigrette and top pizzas with a handful of the greens. Repeat with remaining dough and toppings. Slice and serve!