Add vinegar and peppercorns; bring to a boil over high heat.
Meanwhile, slice about 1 inch off tops of artichokes; discard tips. Trim stems flush with bottoms. Pull off and discard small leaves from bottoms. With scissors, cut thorny tips from remaining outer leaves.
Add artichokes to water and simmer, covered, until bottoms pierce easily, 30 to 35 minutes; drain.
While artichokes cook, make lemonnaise. In a blender or food processor (a blender produces the best results), whirl tofu, lemon juice, oil, and mustard until smooth. Season with salt and pepper. (If making ahead, chill airtight up to 1 day; stir before using.)
Serve artichokes with sauce for dipping.
Varying your dunk sauce: For variations on lemmonaise (step 4 above), add ingredients to the basic recipe and whirl in a blender or food processor until smooth.