1. 1. Prepare the Sourdough Dough: In a large mixing bowl, combine the active sourdough starter, warm water, olive oil, honey (or maple syrup), and salt. Stir until well combined. Gradually add the flour, mixing with a wooden spoon or your hands until a shaggy dough forms.

2. 2. Knead the Dough: Turn the dough out onto a lightly floured surface. Knead for 8-10 minutes until the dough is smooth and elastic. It should spring back when gently poked. If using a stand mixer, use the dough hook attachment and knead on medium speed for 6-8 minutes.

3. 3. First Rise (Bulk Fermentation): Lightly grease a clean large bowl with olive oil. Place the dough in the bowl, turning it once to coat. Cover the bowl with plastic wrap or a clean kitchen towel and let it rise in a warm place for 2-4 hours, or until doubled in size. The exact time will depend on the activity of your starter and your room temperature.

4. 4. Preheat Oven and Prepare Toppings: About 30 minutes before you plan to bake, preheat your oven to 450 F (230 C). If you have a pizza stone or steel, place it in the oven to preheat as well. While the oven heats, chop all your desired vegetables.

5. 5. Shape the Pizza Crust: Gently punch down the risen dough to release the air. Transfer it to a lightly floured surface. You can either divide it into two smaller pizzas or make one large one. Gently stretch or roll the dough into your desired pizza shape (round or rectangular), about 1/4-inch thick. Transfer the shaped dough to a parchment-lined baking sheet or a pizza peel dusted with cornmeal.

6. 6. Second Rise (Proofing) and Topping: Cover the shaped pizza dough loosely with plastic wrap or a towel and let it rest for 30-60 minutes while the oven finishes preheating. This brief second rise helps create a lighter crust. After proofing, spread the pizza sauce evenly over the dough, leaving a small border for the crust. Sprinkle with mozzarella cheese, then arrange your sliced bell peppers, red onion, mushrooms, and cherry tomatoes (and any other optional toppings) over the cheese. Drizzle lightly with a little extra olive oil.

7. 7. Bake the Pizza: Carefully transfer the pizza to the preheated oven (onto the pizza stone/steel or directly on the oven rack if using a baking sheet). Bake for 15-20 minutes, or until the crust is golden brown and the cheese is bubbly and lightly browned.

8. 8. Serve and Garnish: Remove the pizza from the oven. Let it cool for 2-3 minutes before slicing. Garnish with fresh chopped basil before serving.