Make the dough: In the bowl of a stand mixer fitted with the paddle attachment, beat flour, warm water, olive oil, sugar, salt, and yeast at low speed until a shaggy dough forms, about 2 minutes.
Switch to the dough hook attachment. Bead at medium-low speed until a smooth, elastic dough forms, about 10 minutes. (Dough will be very soft but should not be overly sticky.)
Bulk rise: Oil a large bowl. Place dough in bowl, turning to grease top. Cover with plastic wrap, and let rise in a warm, draft-free place (75°F/24°C) until doubled in size, about 30 minutes.
Line a rimmed baking sheet with parchment paper.
Shape bread & add fillings: Turn out dough onto a lightly floured surface, and pat into a 15-inch circle that is thinner around edges than in center. Crumble feta onto dough, leaving a 1-inch border around edges; sprinkle with parsley and dill. Lightly press into dough to adhere. Fold sides of dough over filling to center, pinching seams to seal. Carefully turn dough over, and place on prepared pan. Press dough into a 13x10-inch rectangle.
Final Rise: Cover and let rise in a warm, draft-free place (75°F/24°C) until puffed, about 45 minutes.
Preheat oven to 425°F (220°C).
Add toppings: Brush olive oil onto dough; sprinkle with sesame seeds. Using your fingertips, dimple dough and flatten any air pockets.
Bake: Bake until golden brown and an instant-read thermometer inserted in center registers 190°F (88°C), 15 to 20 minutes. Let cool on pan on a wire rack for 10 to 15 minutes. Serve warm or at room temperature.