Pumpkin Cake with Sage Ice Cream and Pumpkin Cherry Compote

Bring cream, half-and-half, sage, and zest to a boil in a large heavy saucepan over moderate heat. Remove from heat and steep, covered, 10 minutes. Whisk together yolks, granulated sugar, and salt in a large bowl. Whisk in half of hot cream, then whisk egg mixture into remaining cream in saucepan. Cook custard over moderate heat, stirring constantly with a wooden spoon, until it coats back of spoon and reaches 170 °F on thermometer, about 5 minutes (do not let boil). Pour custard through a fine sieve into a bowl and cool, stirring occasionally. Chill custard, its surface covered with plastic wrap, until cold, at least 3 hours. Freeze custard in ice cream maker, then transfer to an airtight container and put in freezer to harden.