Preheat oven to 400F. You'll need either a VERY large baking sheet or two large baking sheets. Sprinkle cornmeal all over the baking sheets to prevent the flatbreads from sticking. If not using cornmeal, make sure to oil the baking sheets well.
In a microwave-safe bowl, combine the thinly sliced red onion and balsamic vinegar. Microwave for 6-8 minutes (or until the onions are softened and resemble caramelized onions), stirring every 2 minutes.
In a large bowl, combine 1 ½ cups self rising flour and Greek yogurt. Mix with a fork until the mixture is all crumbly, then use your hands to work the dough until it becomes a smooth dough. You might need to add more flour (up to ¼ cups) to make the dough not sticky.
Cut the dough in half and form 2 balls of dough. On a large cutting board dusted with flour (all purpose *OR* self rising, doesn't matter!), roll each ball of dough into a 7-8 inch freeform flatbread. Transfer the flatbreads onto your baking sheets sprinkled with cornmeal. If you want, fold the edges of the flatbreads into pleats or fold them under to create a thicker crust. You can also leave them as they are - flat.
Brush each flatbread with olive oil. Top each flatbread with 1/2 of the onion mixture, pieces of goat cheese, fig slices, and fresh thyme leaves.
Bake at 400F for 17-20 minutes. Remove from heat and drizzle with balsamic glaze. Top with additional fresh thyme or sage leaves and serve immediately.
To make your own self-rising flour for this recipe: Combine 1 + 1/2 cups all purpose flour, 2 teaspoons baking powder, and 1 teaspoon salt.If making your own self-rising flour, you can use 1 + 1/2 cups self rising flour and then add up to 1/4 all purpose flour, if needed to get the dough to be not sticky and for rolling - it's OK if the extra bit of flour is not self-rising.