Beat the cream cheese, Dijon and honey together until smooth and easy to spread, with no streaks of mustard left visible.

Lay each tortilla flat and spread the mixture in an even layer right to the edges.

Cover each tortilla with a layer of ham, slightly overlapping the slices so there are no gaps.

Scatter baby spinach leaves over the ham, pressing them down gently so they stick to the filling.

Starting from one edge, roll each tortilla up tightly into a log, keeping the pressure even along the length.

Wrap each log tightly in plastic wrap, twisting the ends like a candy wrapper.

Refrigerate the wrapped logs for at least 2 hours, or overnight, until firm enough to hold a clean slice.

Unwrap and trim the ragged ends off each log with a sharp knife.

Slice each log into rounds about 3/4 inch thick and arrange cut side up on a plate; the spiral should look crisp, not squashed.