Stir together the yeast, 1 tablespoon of the flour, and ¼ cup of the warm water and let stand until surface appears creamy, about 5 minutes.
In a large bowl or in a stand mixer fitted with a dough hook, stir together 1 ¼ cup flour and salt. Add the yeast mixture, oil, and remaining ½ cup warm water and stir until smooth. Stir in enough of the remaining flour so that the dough comes away from the sides of the bowl.
Knead dough by hand or with the dough hook until soft and elastic, about 8 minutes. Form dough into one ball, or 6 if making mini pizzas. Put in a greased bowl and cover loosely with plastic wrap. Let rise in a warm place until doubled, about 1 ½ hours.
With lightly floured hands, shape each dough round into a disk by holding one edge of dough in the air with both hands. Move hands around the edge of dough (like turning a steering wheel), allowing the weight of dough to stretch the round to about 6 inches. Place on a baking sheet lined with parchment paper.
To make the balsamic glaze:
In a medium saucepan, melt the butter over medium heat. Add the onions, carrots, and celery and saute for a few minutes until slightly browned.
Add the wine and thyme sprigs and bring to a boil. Reduce heat and simmer for a one hour until reduced to ½ cup, stirring occasionally.
Strain with a mesh strainer into a small bowl. Stir in balsamic vinegar and add sugar to sweeten, if desired.
To make the candied walnuts:
Put walnuts in a small saucepan and cover with water. Bring to a boil over medium high heat and simmer until slightly softened, about 5 minutes. Drain, then transfer to paper towels to dry completely, about 45 minutes.
Stir together the walnuts and powdered sugar in a small bowl.
Heat the oil in a heavy bottomed sauce pan over medium heat to 350°F. Fry walnuts in small batches until browned, about 2 minutes. Transfer to a baking sheet and sprinkle with salt and cayenne while they are still warm.
To assemble the pizzas:
Preheat grill on high for 10 minutes, covered. Reduce heat to medium high.
Brush the tops of the prepared pizza rounds with olive oil and place face down on the grill. Brush the other side with olive oil. Flip over after 1-2 minutes, when underside is lightly browned. Sprinkle the top with some Gorgonzola cheese and Parmesan cheese and cook for an additional 3 minutes, or until cheese is melted.
Remove from grill and top with some baby arugula, grapes, and candied walnuts, and drizzle with the balsamic port reduction sauce.