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1
Mix about 2 tablespoons of the milk with the cornstarch in a small bowl to make slurry. Whisk the cream cheese and salt in a bowl. Fill a large bowl with ice water.
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2
Mix the remaining milk, cream, sugar, and corn syrup in a large saucepan, bring to a rolling boil over medium-high heat, and boil for 4 minutes. Remove from the heat and whisk in the cornstarch-milk mixture. Bring the mixture back to a boil with a heatproof spatula, thicken slightly, about a minute. Remove from the heat.
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3
Gradually whisk the hot milk mixture into the cream cheese until smooth. Add the olive oil until well blended. Crush the saffron threads between your fingers into the mixture and stir to distribute the threads. Pour the mixture into a 1-gallon Ziploc freezer bag and submerge sealed bag into the ice bath. Let stand, adding more ice as necessary, until cold, about 30 minutes.
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4
Pour the ice cream base into the frozen canister and spin until thick and creamy. Pack the ice cream into a storage container, alternating layers with the Burnt Orange-Caramel Sauce. Work quickly, or the caramel sauce will start to sink. Press a sheet of parchment directly against the surface, and seal with an airtight lid. Freeze in the coldest part of the freezer until firm, at least 4 hours.
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5
Combine the strained, fresh squeezed orange juice, the sugar, and salt to a sauce pan over medium-high heat. I used about 1 and a half oranges. Boil the mixture until the sugar and orange juice thicken and turn honey-colored, about 8 to 10 minutes.
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6
Still on the burner, add the cream and stir to combine, about 30 seconds. Remove from the heat and let cool completely.
