In a large bowl, combine the yeast, sugar, warm water, and olive oil. Add the salt and flour, 1 cup at a time, stirring between each addition, until a shaggy dough forms. Turn dough out onto a well-floured surface and knead until the dough becomes smooth and elastic, 5-7 minutes.
Place dough in a greased bowl, turning to coat the top lightly with oil. Cover lightly with a tea towel and set in a warm place to rise until doubled, about 1 hour.
While dough rises, pour vinegar into a small saucepan. Bring to a boil over medium heat, then reduce heat and simmer, stirring occasionally, until the mixture has reduced to about 1/4 cup. Set aside to cool.
When dough has risen, preheat oven to 450 degrees. If using a pizza stone, place it in the oven to preheat.
Turn dough out gently onto a lightly-floured surface. Divide in half - set aside one half for pizza another time. Roll the remaining half very thinly with a rolling pin, no more than about 1/8 inch thick. Place onto a sheet of parchment paper on an unrimmed baking sheet.
Drizzle dough with olive oil and brush to lightly coat. Top evenly, but not too excessively, with the sliced strawberries, goat cheese, and some of the basil.
Using the baking sheet as a baking peel, transfer the pizza onto your preheated pizza stone. (If not using a pizza stone, just place the baking sheet in the oven). Bake for about 15 minutes, or until the crust is golden and crisp. Remove from oven, drizzle with a couple of tablespoons of the balsamic vinegar (you will have some left over), slice and eat.