Sauté onion in hot oil in a medium saucepan over medium-high heat 3 to 4 minutes or until tender. Stir in garlic, thyme, and red pepper, and sauté 2 minutes. Stir in tomatoes and brown sugar. Reduce heat to medium-low, and cook, stirring occasionally, 15 minutes.
Stir in basil and next 4 ingredients, and cook 5 minutes. Remove from heat, and let cool 15 minutes.
If desired, pulse tomato mixture, in batches, in a food processor 3 to 4 times or to desired consistency. Use immediately, or store in an airtight container in refrigerator up to 3 days.
Note: To make ahead, prepare recipe as directed. Place sauce in an airtight container. Freeze sauce up to 3 months.
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