In a large bowl, mix the honey with the warm water. Stir the yeast in, and let stand for about 10 minutes, until foamy.
Once the yeast mixture is slightly foamy, add the olive oil, salt and the flours. Mix with a wooden spoon until the dough starts to come together. Then transfer the dough out onto a lightly floured surface and knead until the ball of dough becomes smooth, about 10 minutes, adding a little flour at a time if needed. Place the dough in an oiled bowl, and turn to coat the surface. Cover loosely with plastic wrap or a kitchen towel, and let stand in a warm place until doubled in size, about 1 hour. (Caramelize the onions now.)
Preheat the oven to 450F/ 232C and place a pizza stone in the center rack. If you don't have a pizza stone, you can use an inverted baking sheet.
When the dough has doubled, tip it out onto a lightly floured surface, and form into a tight round. Cover again and let rise for about 45 minutes, until doubled.
Roll the ball of dough with a rolling pin or stretch with your hands to desired size/ shape over a lightly floured pizza peel or floured sheet of parchment paper.
Heat the oil and butter in a large skillet over medium heat. Add the onions and stir to coat with the butter and oil. Then spread in an even layer.
Lower the heat to medium-low and cook 30 minutes to an hour, stirring every few minutes to cook evenly. If they are browing too much, lower the heat. Cook until soft, sweet and caramelized. Remove from the heat & set aside.
Spread the caramelized onions in a even layer over the dough. Sprinkle over the minced garlic.
Tear the mozzarella into pieces and sprinkle all over the onions. Then do the same with the burrata. Carefully transfer the pizza to the hot stone or pan. (you can do this by pulling out the oven rack slightly or removing the stone/ pan from the oven. Bake for 10 minutes.
Then carefully spread the fig pieces all over the pizza, drizzle with the remaining 1 tbsp olive oil and sprinkle a little kosher salt and fresh ground pepper on top. Bake for 5-10 minutes more until the cheeses are melted, the crust is golden and crispy on the edges and the figs are starting to get a little color.
Remove from the oven and let rest a couple minutes, then sprinkle the arugula on top, add a dash of red pepper flakes if desired, some fresh shaved parmesan and a nice drizzle of balsamic glaze. Enjoy!
*Balsamic glaze can be purchased at most grocery stores but you can also make it by reducing 1 cup of balsamic vinegar over medium-low heat until thickened and coats the back of a spoon. (this will take about 15 minutes.)
*If transferring the pizza seems intimidating, you can spread the dough on a lightly floured sheet of parchment that is placed over a pizza peel or an inverted baking sheet, then slide the whole sheet of parchment with the prepped pizza onto the hot stone or 2nd inverted sheet pan that is preheating in the oven.