In a medium bowl, combine the minced shallot, lemon juice, and white wine vinegar. Stir and let it sit for about 15 minutes to mellow the sharpness of the shallot. (Thank you Chef Reilly, for this tip!!!)
Add the mustard and honey, whisking until fully combined.
Slowly stream in the avocado oil while whisking continuously until the dressing is smooth and emulsified. Season with salt and pepper to taste.
In a large bowl, add the butter lettuce along with radishes, carrots, croutons, bacon, and Parmesan.
Drizzle with vinaigrette and toss gently until everything is evenly coated. Serve immediately.