Zucchini Scamorza Foccacia

Name: Zucchini Scamorza Foccacia
Ingredients: 1 pack active dry yeast; 1 3/4 cups warm water (should not be too hot to touch); 1 tablespoon sugar; 5 cups a couple tablespoons AP flour; 1 tablespoon salt; 3/4 cup extra virgin olive oil, divided; 2 tablespoons fresh thyme leaves, divided; 1 medium zucchini; 1/2 large ball of smoked mozzarella (scamorza in Italian markets); 1 teaspoon fresh oregano leaves; 1 small clove garlic; 1/2 small shallot; coarse sea salt and freshly ground black pepper for finishing