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Place the apricots in boiling water for 20 seconds to loosen their skins, then remove them from the water, drain and peel them.
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Separate the apricots into halves and discard the pits.
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Chop the apricots coarsely and put them in a large glass bowl.
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Sprinkle with ¼ to ½ cup of the sugar; stir and let stand for 1 hour, then puree them.
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While the apricots are standing, prepare the custard ice cream base.
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Beat the egg yolks in a bowl until they turn a light lemon yellow color, about 3 or 4 minutes. Set aside.
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Combine the whipping cream, milk and the remaining sugar in a heavy-bottom saucepan.
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Cook over medium heat, whisking often, until the sugar has dissolved and the mixture is hot. Ladle about 1 cup of the hot mixture into the beaten egg yolks, whisking constantly until well-blended and smooth.
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Pour the egg yolk mixture into the saucepan and continue to cook over medium heat, whisking constantly, until the mixture thickens enough to form a film or coat the back of a spoon, about 5 minutes.
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Remove from the heat and add the almond extract.
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Let the mixture cool to room temperature, then stir in the pureed apricots.
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Freeze in an ice cream maker according to the manufacturer's instructions