Combine water and 1/2 cup salt in a large bowl, stirring until salt dissolves. Pour salt mixture into a large zip-top plastic bag. Add ice and shrimp; seal. Refrigerate 30 minutes. Remove shrimp from bag; discard brine. Peel shrimp.
Heat oil in a large nonstick skillet over medium-high heat. Add onions and garlic; sauté 15 seconds. Add shrimp, and sauté 1 minute. Add wine; cook 1 minute, scraping pan to loosen browned bits. Add tomato, 1/4 teaspoon salt, and pepper; cook 3 minutes or until shrimp are done. Remove from heat; serve over pasta. Sprinkle with basil.