Heat 2 Tbsp. extra-virgin olive oil in a large Dutch oven or other heavy pot over medium-high. Cook 2 shallots, finely chopped, until slightly softened, about 3 minutes. Add 3 garlic cloves, thinly sliced, and 1 tsp. Diamond Crystal or ½ tsp. Morton kosher salt and cook, stirring often, until softened and fragrant, about 3 minutes.
Add 1 lb. orzo and cook, stirring often, until toasted and golden in spots, about 3 minutes. Add 1 cup dry white wine and 1 tsp. Diamond Crystal or ½ tsp. Morton kosher salt. Season with lots of freshly ground pepper; cook, stirring often, until liquid is absorbed, about 2 minutes.
Cook orzo, adding 5 cups water a cupful at a time, stirring often and waiting until absorbed before adding more, until almost tender, about 15 minutes total. Add 6 oz. sugar snap peas, strings removed, thinly sliced, ½ cup frozen peas, thawed, and another ½ cup water; cook, stirring often, until vegetables are crisp-tender and orzo is cooked through, 2–3 minutes. (Orzotto will continue to thicken as it cools.) Remove from heat, add 1 oz. Parmesan, finely grated (about ½ cup), 4 Tbsp. unsalted butter, cut into small pieces, and 3 Tbsp. fresh lemon juice, and stir until combined and melted. Taste and season with more salt and pepper if needed.
Divide orzotto among shallow bowls and swirl a little of ½ cup store-bought pesto into each; sprinkle with more pepper.