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Generously grease and flour a bundt pan (do not preheat the oven).
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Beat sugars and butter at medium speed with an electric mixer until light and fluffy, about eight minutes.
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Add oil, and beat until blended.
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Add eggs, one at a time, beating just until incorporated.
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Combine flour, baking powder, and salt in a small bowl.
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Alternate milk and flour mixture in thirds, beginning and ending with flour mixture.
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Beat at low speed just until blended after each addition.
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Stir in vanilla extract.
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Pour batter into prepared bundt pan.
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Bake at 325° for 1 hour and 20 minutes (check with a wooden pick at around an hour--a few moist crumbs should cling to the pick).
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Cool in pan on wire rack 10 minutes.
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Invert from pan and cool on wire rack.
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While cake cools, stir milk into powdered sugar.
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Melt caramel sauce in a microwave until pourable and whisk into the icing.
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When cake is completely cool, slowly pour icing over cake (put a piece of foil or parchment underneath the rack to make cleanup easier).
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Let set and enjoy.