To prepare the dressing, place the chopped garlic, shallots, Dijon mustard, vinegar, roasted garlic, and rosemary in a small bowl and whisk together. Slowly whisk in the olive oil until the dressing is emulsified and thickened. Season to taste with salt and pepper.
Refrigerate until ready to use. The dressing may be stored in the refrigerator in a tightly-covered container for up to 3 weeks.
To prepare the salad, wash and dry the lettuces, tear the leaves into pieces, and place in a large salad bowl. Add the cucumber, tomato, radishes, and onion and toss well.
Add about 1/4 cup of the dressing, or enough to lightly coat the leaves, and toss well to coat evenly. Serve immediately.