Herby Pizza with Carrot Top Pesto

Name: Herby Pizza with Carrot Top Pesto
Ingredients: 2 tsp. sugar; ½ tsp. active dry yeast; 2¼ cups bread or all-purpose flour; 1½ Tbsp. extra-virgin olive oil, plus more for drizzling; 2 tsp. kosher salt; ⅓ cup coarsely grated Parmesan; 1 small garlic clove, grated; 1 Tbsp. fresh lime juice; 1 cup basil leaves, plus more for serving; 1 cup tender carrot tops, plus more for serving; ⅓ cup extra-virgin olive oil, plus more for drizzling; ¼ cup mint leaves, plus more for serving; Kosher salt; 4 medium carrots, finely sliced on a mandoline, divided; ½ serrano chile, very thinly sliced, divided; Pea shoots and/or blue basil (for serving)