Make the vinaigrette: Whisk the lemon juice, Dijon, garlic, and shallot together in a medium bowl. Gradually whisk in the olive oil in a steady stream until emulsified. Season with salt and pepper.
For the sandwich: Combine the radishes, cucumber, scallions, olives, capers, lettuce, and artichoke hearts (if using) in a salad bowl. Drizzle in ⅓ of the vinaigrette and toss to coat. Add more vinaigrette as needed to coat the salad lightly.
Split the ciabatta lengthwise using a serrated knife and tear out most of the bread from the middle of both halves (save to use in the gazpacho or to make breadcrumbs for future use).
Arrange ⅔ of the salad on the bottom bread half. Layer the tomato, eggs, tuna, and anchovies evenly down the loaf, then top with the remaining salad (as much as will fit).
Spoon some of the remaining vinaigrette over the cut side of the top bread half to coat lightly, then drizzle more vinaigrette (including what’s left in the salad bowl) over the filling. Close the sandwich.
Wrap the entire sandwich tightly in plastic wrap and place it on a tray or baking sheet in case of leaks. Weight it evenly with a baking sheet topped with canned goods (or use two heavy pans, side by side). Refrigerate for at least 6 hours and up to overnight. Cut into wedges to serve.