Place yolks, lemon juice, garlic, honey, salt, and chipotle in a small food processor or use a vessel that will work with an immersion blender.
With the processor or blender running, slowly pour in the oil. Process until aioli forms and thickens, about a minute.
Pour the aioli into a plastic bag and clip one corner of the bag, clipping a very small piece of the corner from the bag. Using the bag like a pastry bag, drizzle the aioli over the mushrooms. Reserve the remaining aioli for added dipping if desired.