1. Dough: In bowl, stir together 1/4 cup flour, warm water, yeast and sugar; let stand for 5 to 10 minutes or until mixture starts to look bubbly and frothy. Using wooden spoon, stir in olive oil, remaining flour and salt to make loose dough. Transfer to lightly floured surface; knead for 10 to 15 minutes, adding flour as needed, to make soft, elastic, and slightly sticky dough.
2. Form dough into ball; transfer to lightly greased bowl. Brush top of dough lightly with oil; cover with wet kitchen towel. Let stand in warm spot for about 2 hours or until doubled in size. Punch down dough; transfer to airtight container or resealable plastic bag. Refrigerate overnight; let stand at room temperature for 2 hours.
3. Toppings: Preheat oven to 450ºF. Heat 2 tbsp olive oil in large skillet set over medium heat; cook onion, butter and 1/4 tsp salt, stirring frequently, for 20 to 25 minutes or until deep golden brown. Remove from heat and set aside.
4. On lightly floured surface; roll out dough into 8-inch round. Using hands, stretch dough into 12-inch round, about 1/4-inch thick. Transfer to lightly greased 12-inch pizza pan.
5. Sprinkle 1/2 cup shredded mozzarella over dough. Top with chicken, caramelized onion and goat cheese. Sprinkle with remaining mozzarella. Bake, rotating pan halfway through, for 20 to 25 minutes or until edges are golden brown and cheese is melted.
6. Meanwhile, in food processor, pulse together basil, pine nuts and garlic until well combined. Slowly add remaining olive oil, pulsing until smooth. Stir in Parmesan, pepper and remaining salt.
7. Drizzle 3 tbsp of the pesto over pizza.
Leftover pesto can be transferred to airtight container and refrigerated for up to one week. Spoon over grilled meats and fish, or toss with pasta.