Let cream cheese come to room temperature. Thaw spinach and firmly drain by pressing with back of spoon to remove excess moisture.
In bowl, mix spinach, cream cheese, horseradish, allspice, and pepper. Add sour cream as needed for workable consistency. Adjust seasonings to taste.
With spatula, spread mixture evenly to cover each tortillas. Divide ham into 6 equal portions. Layer one portion of ham on each tortilla covering spinach mixture.
Roll each tortilla tightly to encase filling. If made ahead, cover with plastic wrap and chill overnight. Cut each tortilla diagonally with sharp knife into 3/4" slices.
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