Combine the warm water, sugar, and yeast in a bowl and let it sit for 10 minutes until foamy—this activates the yeast and ensures a well-risen crust. In another bowl, mix the flour and salt together, then add the foamy yeast mixture and olive oil. Stir until a shaggy dough forms, then knead by hand for 5 minutes until smooth and elastic. Form the dough into a ball, place it in an oiled bowl, cover loosely, and let it rise for 1½ to 2 hours until doubled in size. I like to do this rise time while preparing the other components so nothing sits idle.
While the dough rises, combine the balsamic vinegar, maple syrup, and honey in a small saucepan. Simmer over medium-low heat for 15–20 minutes, stirring occasionally, until reduced by half and slightly syrupy—this concentrates the flavor and adds a sweet-tart complexity to the pizza. In a separate large skillet, heat 1 tablespoon of olive oil over medium heat and add the thinly sliced onions with a pinch of salt. Cook for 5–7 minutes, stirring occasionally, until they begin to soften and turn golden. Add the ¼ cup water to deglaze and prevent sticking, then add another tablespoon of olive oil and ½ teaspoon of salt. Continue cooking for another 5 minutes until the onions are deeply caramelized and sweet. I find this low-and-slow method for onions develops a richer flavor than rushing them on high heat.
About 20 minutes before you're ready to bake, preheat your oven and pizza stone to 450°F. Once the dough has finished rising and the oven is hot, turn the dough out onto a lightly floured surface. Gently stretch and roll it into a 13-inch round, then use a fork to poke small holes across the surface—this prevents large air bubbles from forming during baking. Dust a pizza peel or baking board generously with cornmeal, then carefully transfer the stretched dough onto it.
Lightly brush the entire dough surface with the remaining 1 tablespoon of olive oil. Spread the caramelized onions from Step 2 evenly over the crust, leaving a small border for the crust edge. Scatter the stemmed and quartered figs across the top, then crumble the goat cheese into small pieces and distribute them throughout. Slide the pizza onto the preheated stone and bake for 10–12 minutes until the crust is golden brown and the cheese is warm and slightly bubbling around the edges.
Remove the pizza from the oven and let it rest for 1 minute. Toss the arugula with the fresh thyme leaves, a small drizzle of the remaining olive oil, and a pinch of salt and pepper. Top the hot pizza with the dressed arugula so it wilts slightly from the residual heat, then drizzle the balsamic reduction from Step 2 over the top in a light pattern. Slice and serve immediately.