Step 1

Preheat the oven to 300 degrees. Place the tomatoes in a baking dish large enough to fit them in a single layer. Add the salt and sugar, and toss together. Add the regular olive oil, and toss again. Place in the oven for 45 minutes until the skins have shriveled and just split; the tomatoes should still be still intact. Remove from the heat, and allow to cool.

Step 2

Bring a pot of water to a boil, and salt generously. Fill a medium bowl with ice water. Place the basil in the boiling water, and blanch for 15 seconds. Remove with a skimmer, and transfer to the ice water. Drain and squeeze out excess water, then place on a clean dish towel and again squeeze out as much water as you can. Place in a blender with the olive oil. Blend one to two minutes until the olive oil is green and tinged with flecks of basil. Transfer to a squeeze bottle, and refrigerate.

Step 3

Arrange the tomatoes on a platter. Drizzle the bright green basil oil decoratively around and over them, and pour on any juices from the pan. Serve warm or at room temperature.