Whip cream with confectioner's sugar until soft peaks form. Whisk in amaretto or almond extract. Refrigerate until ready to use.
Melt butter in a large saute pan over medium heat. Add sugar; stir to dissolve. Swirl occasionally until mixture is light brown, 3 to 5 minutes.
Add apricots, cut side down. Increase heat to medium high, and cook until sugar has turned a deep amber and apricots are well caramelized, no more than 5 minutes. Shake pan a few times.
Remove pan from heat and transfer apricots to a plate, cut side up. Whisk milk into sugar mixture to make caramel sauce. Simmer over low heat until thick, 2 to 3 minutes.
Arrange apricots on four plates and pour sauce over each one. Spoon almond cream on the side and garnish with sliced almonds.
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