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Preheat oven to 450 degrees.
Heat oil in large nonstick skillet over medium. Add shallot and cook 1 to 2 minutes, stirring occasionally, until soft. Add mushrooms and garlic; cook 5 to 6 minutes, stirring often, until liquid has almost evaporated. Remove from heat. Sprinkle with 1/8 teaspoon sea salt; set aside.
Coat baking sheet or pizza pan with thin layer olive oil or a dusting of cornmeal. On clean working surface dusted with flour, gently stretch pizza dough to fit pan: roughly a 12" circle or 10" x 6" rectangle will do. Gently place dough in pan; pierce well with fork. Lay out bocconcini slices and spread mushroom mixture on top.
Place pizza in preheated oven and bake 13 to 14 minutes.
Toss arugula with lemon juice and a drizzle olive oil. Remove pizza from oven, top with arugula and season with sea salt and pepper.