Place berries in a blender container or food processor bowl. Cover and blend or process until nearly smooth.
Combine 3 cups of the milk, the sugar, and egg yolks in a large saucepan. Cook and stir over medium heat until mixture coats a spoon. (To test, dip a spoon into the custard and draw a line with your finger through the coating. The custard is done when the edges along the line keep their shape.) Remove from heat. Stir in the remaining milk, the pureed berries, and, if desired, food coloring.
Cover surface of gelato mixture with plastic wrap. Refrigerate 8 hours or overnight until chilled. (Or, place saucepan in a sink of ice water to cool quickly; then cover and chill for 2 hours.) Freeze mixture in a 4- or 5-quart ice cream freezer according to manufacturer's directions. Ripen for 4 hours.