Purée basil, parsley, tarragon, mayonnaise, sour cream, lemon zest, 2 Tbsp. lemon juice, and 2 Tbsp. oil in a blender until very smooth and pale green.
Transfer dressing to a medium bowl and add tuna. Using a fork, break up tuna and incorporate into dressing.
Mix in celery, shallot, and garlic; season with salt and lots of pepper.
Toss chopped mixed herbs with remaining 1 tsp. lemon juice in a small bowl. Drizzle with a little oil, season with salt and pepper, and toss again.
Build sandwiches with English muffins, tuna salad (you may have a bit extra), and herb salad.
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