Heat oven to 375°F (190°C).

Line a 15x10x1-inch baking pan with foil and grease the foil with shortening or cooking spray.

In a medium bowl, beat the eggs with an electric mixer on high speed for about 5 minutes or until very thick and lemon-colored.

On low speed, gradually beat in 1 cup granulated sugar.

Beat in ⅓ cup water and 1 teaspoon vanilla.

Gradually add flour, baking powder, and salt, beating just until the batter is smooth.

Pour the batter into the prepared pan, spreading to the corners.

Bake for 12 to 15 minutes or until a toothpick inserted in the center comes out clean.

Immediately loosen the cake from the edges of the pan and invert it onto a towel generously sprinkled with powdered sugar.

Carefully remove the foil.

Trim off stiff edges of the cake if necessary.

While hot, carefully roll the cake and towel from the narrow end.

Cool on a cooling rack for at least 30 minutes.

In a chilled medium bowl, beat the whipping cream, 2 tablespoons granulated sugar, and 1½ teaspoons instant coffee granules on high speed until stiff peaks form.

Unroll the cake and remove the towel.

Spread the filling evenly over the cake.

Roll up the cake again.

In a medium bowl, beat the cocoa and butter with an electric mixer on low speed until well blended.

Gradually beat in the powdered sugar.

Beat in 1½ teaspoons vanilla and enough hot water, one teaspoon at a time, until the frosting is smooth and spreadable.

For the tree stump, cut off a 2-inch diagonal slice from one end of the cake.

Attach the stump to one long side using 1 tablespoon of frosting.

Frost the entire cake with the remaining frosting.

Using the tines of a fork, make strokes in the frosting to look like tree bark.

Decorate your yule log with sugared cranberries and rosemary sprigs.

Dip fresh cranberries and rosemary sprigs in a mixture of light corn syrup thinned with a bit of water, then roll in granulated sugar.

Let stand until set.

Arrange around the log on a serving platter or on top of the log.

You can also sprinkle chopped pistachios over the frosting.