Dissolve the sugar, yeast, salt and olive oil in the warm water.
Add the flour and mix until combined.
Turn out the dough on a lightly floured surface and knead the dough for about 7 minutes, or until the dough is smooth.
Transfer to an olive oil-greased bowl, lightly cover and place in a warm place to rise for 1 hour. I like to proof my dough in a 100°F oven.
When the pizza dough has doubled in size, divide the dough in half and form into two balls of dough.
Make the pizza:
Place the potatoes in a small saucepan and add enough water to just cover the potatoes. Season with some kosher salt. Bring to a boil, then cover and lower heat to a simmer. Cook for about 15 minutes, or until the potatoes are fork-tender, but not mushy. Drain the potatoes and slice into 1/4 inch coins.
Roll out 1 ball of pizza dough to about 1/4 inch thickness and a diameter of about 14 inches. Lightly brush the dough with olive oil. Spread about 1/4 cup of the pesto on the dough, leaving a 1/2 inch border around the perimeter. Top with potatoes, Brussel sprouts, and yellow squash. Season with salt and pepper and drizzle lightly with olive oil. Top with cheese.
Repeat for the other ball of dough.
Bake in a 475°F oven for about 8-9 minutes, or until the crust is golden. Sprinkle a little more cheese on the top, slice and serve immediately.
Can I use store-bought pizza dough? Yes! This will save time!
Can I freeze this? Yes, you can make the pizza dough in advance and freeze it until you are ready to make your dough, just defrost overnight in the refrigerator. You can also assemble the entire pizza, wrap it well in plastic wrap and freeze. Add a few minutes to the baking time and bake from frozen.
What kind of potatoes should I use? I recommend mini baby potatoes, for its edible skin and since it cooks quickly. When sliced, the small rounds are the perfect size (like pepperoni!). If you have other varieties of potato on hand, just be sure to cook them appropriately. Yukon gold potatoes also work beautifully here.