In a medium nonstick skillet, heat oil over medium heat. Add onion and cook 4 minutes or until softened. Stir in 2 cups tomatoes, honey, vinegar, 3 Tbsp. ginger, paprika and cumin. Simmer 7 minutes or until thickened and jam-like. Set aside to cool, at least 20 minutes. Stir in chopped basil.
Unwrap both bries, and slice the top rind off of the other. Place the first Brie, rind side down, on a serving plate. Spoon tomato-ginger jam mixture on the cut side of the first Brie, and spread evenly on the cut surface. (Refrigerate any additional Tomato-Ginger Jam for up to a week, and serve it as an accompaniment to a cheeseboard with baguette, or as a spread for crackers or breadsticks.) Top with a second Brie, cut-side down.
Toss together remaining tomatoes and ginger to garnish top of Brie. Add fresh basil and serve.
Prepare tomato-ginger jam up to 6 days in advance, store refrigerated. Bring to room temperature or microwave 30 seconds before using.