In skillet, preferably nonstick, heat oil over medium heat. Add shallot and cook stirring occasionally til softened, about 1 minute. Add cherry tomatoes and cook til hot an beginning to soften, about 2 minutes. Remove from heat and season with salt and pepper. Transfer tomato mixture to a bowl an cover to keep warm. In bowl, whisk together eggs, 1 Tbsp. of the basil, 3/4 tsp. salt and 1/4 tsp. pepper til thoroughly blended. Do not overbeat. Add butter to skillet and melt over medium low heat. When butter is hot, add egg mixture to pan and cook til eggs begin to set, about 20 seconds. Stir with a heatproof spatula, scraping up the eggs on the bottom an sides of pan and folding them toward the center. Repeat til eggs are barely cooked into moist curds. Add cherry tomato mixture and the mozzarella and stir to distribute throughout the eggs. Remove pan from heat and let eggs stand in pan to allow the residual heat to finish cooking them and melt the mozzarella, about 1 minute. sprinkle remaining 1 Tbsp. basil over the scramble and serve at once. this is an easy dish to toss together. The trick is to scramble the eggs til barely set, remove pan from heat and let the eggs finish cooking with the residual heat of the pan. This is a great summer breakfast, when cherry tomatoes and sweet basil are at their best.