Cut eggs in half crosswise (not lengthwise as commonly instructed for deviled eggs) to produce 2 round halves. Trim a little off the more pointed end of each half so that they will sit flat on serving dish.
Carefully remove yolks from egg halves and mash in a bowl with a fork. Add dip, cheese and hot pepper sauce, if desired; mix until smooth.
Add chopped ham and stir until well combined.
Spoon mixture evenly into egg whites.
Garnish with paprika and chives, if desired.
Cover and refrigerate until ready to serve. Serve chilled.
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