In the bowl of a stand mixer fitted with the dough hook attachment. Stir together water and honey, then sprinkle over active dry yeast. Let bloom until foamy, about 10 minutes, then stir in ¼ cup olive oil.
Add flour, salt, basil, mint and thyme to the bowl and mix on medium speed until a smooth dough forms. Using greased hands, transfer to a greased bowl. Cover and let proof in a warm place until doubled in size, about 1 hour.
Preheat oven to 450°F and place a baking steel or pizza stone on the middle rack. Transfer proofed dough to a greased sheet pan and using your hands, spread to fit the pan, then make dimples in the dough with your fingers. Arrange zucchini and summer squash over the dough, alternating between the two and leaving a 1-inch border around the dough. Cover again and let proof again until puffed, 45-60 minutes.
Drizzle the remaining ¼ cup olive oil over the sliced squash and dough, then garnish with flaked sea salt and aleppo pepper. Place directly onto the baking steel or stone and bake until golden and and an internal temperature of 195°F is reached, 30-35 minutes. Let cool completely, then slice into squares and serve.
