Prepare a bowl of ice water. In a separate bowl, pour boiling water over basil leaves. Let the herbs steep for 30 seconds.
Using tongs or a slotted spoon, transfer the basil from the hot water to the ice bath to halt the cooking process. By shocking the basil, you will retain its deep green color.
Remove the leaves from the ice water and squeeze out any excess water using a paper towel.
Place the herbs in a blender or food processor and add the oils. Blend for 1 minute.
Place the combined mixture in a small sauce pan over medium heat. Stirring constantly, warm for 1 to 2 minutes. Do not let it boil.
Strain contents through a fine meshed sieve. If you do not have a fine sieve, strain through several layers of cheesecloth.
Let the basil oil come to room temperature before serving. Oil will keep for a week, refrigerated.
Notes
* Grapeseed oil has a lighter taste and will allow the delicate flavors of the basil to shine through. The olive oil adds richness and body.