Hard-cook the eggs. Place eggs in a saucepan and cover with cold water by 1 inch. Bring to a boil, cover, turn off heat, and let sit 10 to 12 minutes (10 for slightly softer yolks, 12 for fully set). Transfer to ice water, cool, then peel.
Make the cucumber dill spread. In a bowl, mix cream cheese, mayo (or yogurt), dill, lemon zest, lemon juice, salt, pepper, and optional garlic until smooth. Thinly slice cucumber and pat dry with paper towels.
Make the egg salad. Chop eggs (small dice for neat sandwiches). Stir with mayo, Dijon, pickles or relish, chives, salt, pepper, and optional paprika. Taste and adjust. You want it bright and seasoned.
Make the ham and cheddar spread. Stir mayo, Dijon, and honey (if using) with a few cracks of black pepper. This becomes the glue so the ham does not slide around.
Plan your loaf (so the yield makes sense). For a three-flavor platter, use 6 slices per filling (18 total). That makes 3 whole sandwiches per filling, or 9 whole sandwiches total. Cut each into 3 rectangles for 27 pieces (right in that 24 to 30 sweet spot). If your loaf is 20 slices, use the extra 2 slices to make one bonus sandwich in your favorite flavor.
Set up the bread. Lay bread slices on a cutting board. Spread a thin layer of softened butter or mayo on each slice. This is your anti-soggy insurance policy.
Assemble the cucumber sandwiches. Spread cucumber dill mixture on both slices (thin layer). Add a single layer of cucumber to one slice, then top with the other slice. Press gently so everything sticks.
Assemble the egg salad sandwiches. Spoon egg salad onto a slice and spread evenly to the edges. Top with another slice and press gently.
Assemble the ham and cheddar sandwiches. Spread the mustard-mayo on both slices. For extra stability (and less slide), put cheddar against the bread, then add ham folded into loose ribbons (better texture than laying flat). Top with bread and press gently.
Chill for clean cuts. Stack each sandwich type on a plate or sheet pan, cover, and chill 15 to 20 minutes. This firms everything up so your knife glides instead of dragging.
Trim and slice. Use a serrated knife. Trim crusts if desired, then slice each sandwich into 3 rectangles or 4 triangles. Wipe the knife between different fillings for the cleanest look.
Serve. Arrange on a platter, cover lightly with plastic wrap until serving, and let sit at room temp about 10 minutes for the best texture and flavor. For food safety with egg salad and other mayo-based fillings, do not leave them out for more than 2 hours total (or 1 hour if it is hot out). When in doubt, rotate in a fresh chilled platter.
If you are serving these for guests, group each flavor together and alternate shapes. Triangles feel classic, rectangles feel modern. Both feel like you had your life together.
