Step 1Pit and chop the plums (you should have about 4 cups). Place them in a mixing bowl with the sugar and stir to combine. Set aside 30 minutes to macerate, stirring occasionally.
Step 2Crush the peppercorns and allspice with a heavy pan or with 1 or 2 pulses of a spice grinder. Leave in large pieces so they can be strained out later. Combine the spice mixture, milk, cream and salt in a small saucepan and bring to a simmer over medium heat, about 3 minutes. As soon as bubbles appear around the rim and a skin forms on top, remove from the heat and cover. Set aside 30 minutes to steep.
Step 3Place the fruit in a blender and strain the cream mixture over the top, discarding the spices. Puree until smooth. Bits of peel should be visible. The mixture will be slightly thinner than a milkshake. Pour into a bowl and chill for 30 minutes.
Step 4Freeze in an ice cream maker according to manufacturer's instructions. The mixture will get to the texture of soft-serve ice cream. Spoon it into a container, cover and place in the freezer for another hour to ripen. Serve immediately. If the ice cream is left overnight, it may become icy, in which case you should allow it to warm slightly outside the freezer before serving.