To prepare the aioli, place the first 6 ingredients in a food processor and pulse until smooth. Transfer aioli to a bowl; cover and refrigerate until needed. Preheat your grill to medium-high. Brush the asparagus with the oil. Grill 1 minute per side, or until lightly charred. Arrange the asparagus on a platter with the red pepper aioli alongside.
Note: Roasted red peppers are sold in jars or in bulk. To blanch the asparagus spears, cook in boiling water 1 minute. Drain well, cool in ice-cold water, drain well again, and pat dry.