Blend: Cut off the stems and put the jalapeños into a blender. Pour in the oil and blend on the highest setting until only tiny pieces are left. The finer it is, the more color and flavor end up in the oil.
Cook out the water: Pour everything into a medium pot and heat it over medium heat to around 100 °C (212 °F). Let it simmer there, stirring now and then, until it stops sizzling, about 10 minutes. That's the sign all the water from the jalapeños has evaporated. The more water in there, the longer it takes. Keep the heat at medium, nothing should brown.
Cool: Optional: for a stronger flavor, take the pot off the heat and let it sit for 30 minutes. Then set the pot in a bowl of ice water and stir until the oil is almost cold.
Strain: Pour the oil through a fine-mesh sieve to catch the coarse bits.
Filter: Line a second sieve with a coffee filter, set it over a bowl and pour in the oil. Let it drip through on its own, plan at least 30 minutes. The more tiny bits are left, the longer it takes. Don't press it, or the oil turns cloudy.
Bottle: Pour the oil into a clean bottle. Store in the refrigerator for up to one week.