In a sauce pan, heat 1 cup of the olive oil over medium, then add in the jalapeño halves. Let them simmer in the oil over medium for 5 minutes, stirring frequently.
Add the remaining oil and reduce the heat to low. Continue stirring for 5 minutes.
Remove the saucepan from the heat, cover, and allow the oil to rest and cool for 1 hour.
Strain the oil into a bottle or jar to remove the jalapeño pepper halves and seeds.