My take on those boozy treats that weigh down suitcases returning from Jamaica, this moist cake packs a rum punch. You may wish to card your guests before serving. The longer the rum soaks in, the better—overnight is best.
Preheat oven to 325°. Cream butter and sugar until light and fluffy, 5-7 minutes. Add eggs, 1 at a time, beating well after each addition. Beat in extract. In a small bowl, combine rum and milk. In a large bowl, whisk flour, pudding mix, cornstarch, baking powder and salt; add to creamed mixture alternately with rum mixture, beating well after each addition.
Transfer to a greased and floured 10-in. fluted tube pan. Bake until a toothpick inserted in center comes out clean, about 1 hour. Cool 10 minutes. Remove from pan briefly to prevent sticking; replace in pan. Cool on wire rack.
Meanwhile, for syrup, heat butter, water, sugar and salt in a small saucepan over medium heat. Bring to a boil, stirring constantly. Remove from heat; add rum and extract.
Using a small skewer, poke holes in cake. Slowly pour syrup over cake until all syrup is absorbed. Cover; let cake stand overnight.