Combine all the pesto ingredients in a food processor and blend until smooth. Drizzle in a bit more tea or olive oil as needed for proper consistency.
Right before serving, place tortilla on a plate, then spread with cream cheese and pesto. Top with ham slices, then roll into a tight log. (Use a bit of cream cheese to seal the edge if needed.) Cut off both ends, then slice remaining log into 1” slices and arrange on serving platter. Makes about 2 dozen pinwheels.