With bright sweetness from tomatoes and a savory, robust finish from garlic, this mild, lightly acidic vinegar is ideal for finishing dishes. Drizzle over vegetables, soups, or fish.
Combine wine, white wine vinegar, basil leaves, mashed tomatoes, and garlic in a 1 ½- to 2-quart glass jar, leaving at least 1 inch of headspace at the top. Place a quadruple layer of cheesecloth or a clean kitchen towel over top of jar, and secure firmly using kitchen twine or a rubber band.
Store in a cool, dark, dry place, stirring weekly, until a web-like “mother” forms, up to 4 weeks. Let stand, undisturbed, until wine has acidified, 3 to 4 months.
Place a fine wire-mesh strainer over a large bowl; line with a double layer of cheesecloth. Carefully pour vinegar mixture through strainer, stirring without pressing on solids, until all liquid has passed through. Discard solids. Pour vinegar into an airtight bottle; store in refrigerator.
Tomato-Chardonnay vinegar may be refrigerated up to 6 months.