1. Combine the pineapple and 1/2 cup of the sugar in a nonreactive bowl. Let sit for 2 hours to draw out the juices. Stir occasionally. Mash pineapple with a potato masher, and add the milk. Transfer to a pot and cook over low heat, without boiling, until sugar is dissolved, about 4 minutes. Set aside and let cool.

2. Beat the egg and egg yolks at high speed until light in color, about 2 minutes. Gradually add the remaining 1/4 cup sugar. Lower the speed and mix in the cream. Pour the pineapple-milk mixture through a strainer and add 1 1/2 cups of the liquid to the egg-cream base. (Reserve 1/4 cup pulp, discarding the rest.)

3. Chill, then pour into an ice-cream maker and freeze according to manufacturer's instructions. When ice cream is frozen, fold in the reserved pineapple pulp.