Preheat oven to 350°. Lightly butter and flour a 10-inch bundt pan.
Cook amaranth in very hot skillet, 1 tablespoon at a time, stirring constantly, until it pops, 10 to 15 seconds per tablespoon. Set aside.
Beat butter with shortening with an electric mixer until light and fluffy. Slowly beat in 2 cups of sugar. Add eggs, one at a time, beating thoroughly after each addition. Beat in lime zest and 1½ teaspoons of vanilla. Stir in popped amaranth.
Sift flour with baking powder and salt 2 times. Add to batter in 3 parts, alternating with 3 parts of the milk. Spoon batter into the prepared bundt pan.
Bake cake until a toothpick inserted in the center comes out clean, about 1 hour.
Meanwhile, combine the remaining ¼ cup sugar with the lime juice and the remaining ¼ teaspoon vanilla in a small saucepan. Cook over medium-low heat until the sugar dissolves. Keep warm.
When the cake is done, place the pan on a rack. Prick holes in the cake, and pour the warm lime mixture over. Let the cake cool on the rack for 15 to 20 minutes before unmolding. Serves 10.