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1
In a heavy saucepan, bring cream and milk to a simmer. Stir in lemon peels and ginger, cover, and remove from heat. Let steep for 1 hour.
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2
Puree blackberries in a blender or food processor just until they break apart into a liquid and no large chunks remain (see note). Slowly pour puree through a strainer and gently stir with a fork or whisk. Measure out 1 1/2 cups strained juice and discard blackberry pulp.
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3
In a heavy saucepan, bring strained blackberry juice to a simmer on medium heat and reduce to 1/2 cup, stirring frequently. Stir in 1/2 cup sugar and 1/4 teaspoon salt until dissolved. Transfer to a small container and chill in refrigerator.
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4
In a clean, heavy saucepan, whisk together 3/4 cups sugar with egg yolks until pale in color and thickened. When dairy finishes steeping, pour through a strainer into pot and whisk to combine with yolk-sugar mixture. Put saucepan on medium heat and cook, stirring frequently, until a custard forms on the back of a spoon, but a finger swiped across the back leaves a clean line. Add 1/2 teaspoon salt. Pour through a stainer into an airtight container and refrigerate overnight.
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5
The next day, churn in ice cream maker according to manufacturer's instructions. While ice cream is churning, remove blackberry syrup from freezer and stir to loosen. Transfer 1/3 of finished ice cream into an airtight container, then quickly spread on half of syrup. Repeat, and top off with last 1/3 of ice cream. Chill in freezer until firm, at least three hours, preferably longer.
