Preheat oven to 375°. Line a greased 15x10x1-in. baking pan with waxed paper. Grease paper; set aside.
Beat eggs 3 minutes. Gradually add granulated sugar; beat until mixture becomes thick and lemon-colored, about 2 minutes. Stir in water, 1 teaspoon almond extract and 1/2 teaspoon vanilla. In another bowl, combine dry ingredients; fold into egg mixture. Spread batter evenly in prepared pan.
Bake until cake springs back when lightly touched, 12-15 minutes. Cool 5 minutes. Invert onto a kitchen towel dusted with confectioners' sugar. Gently peel off waxed paper. Roll up cake in the towel jelly-roll style, starting with a short side. Cool completely on a wire rack.
Meanwhile, beat cream, confectioners' sugar and remaining extracts until soft peaks form. Refrigerate half of the whipped cream. Chop 1 cup almonds; fold into remaining cream. Unroll cake; spread with jam to within 1/2 in. of edges. Top with almond mixture.
Roll up again. Place seam side down on a serving platter. Frost top, sides and ends with remaining whipped cream. Refrigerate, covered, about 1 hour. Top with remaining almonds; serve, if desired, with raspberries and mint.
To toast nuts, bake in a shallow pan in a 350° oven for 5-10 minutes or cook in a skillet over low heat until lightly browned, stirring occasionally.