For the cake: Preheat the oven to 350 degrees F. Grease a 9-inch round cake pan with butter and dust with flour, tapping out the excess. In a medium bowl, whisk together the flour, baking powder and salt; set aside.
Beat the butter in a large bowl with an electric mixer on medium speed until fluffy, about 2 minutes. Add the sugar and continue to beat until very fluffy, about 2 minutes longer. In a small bowl, whisk together the cream and eggs. Add half the flour mixture and half the egg mixture to the creamed butter and beat until combined. Repeat with the remaining flour and egg mixture. Add the lemon zest and vanilla and beat the batter on medium-high speed for an additional 1 to 2 minutes.
Transfer the batter to the prepared cake pan, spread the top evenly and bake until a toothpick inserted into the center comes out clean and the top sprigs back to the touch, 40 to 45 minutes. Cool in the pan 10 minutes, then turn out onto a wire rack and cool completely.
For the filling: Combine the rhubarb with 1/2 cup of the sugar and 1/4 cup water in a medium pot. Bring to a simmer over medium heat and continue to cook, stirring, until the rhubarb cooks down into a thick puree, 18 to 20 minutes. Cool completely, then fold in half of the strawberries. Stir the remaining 1 tablespoon sugar into the remaining berries.
For the whipped cream: When ready to assemble the cake, whip the cream with the sugar and vanilla in a medium bowl with a mixer until stiff peaks form.
Using a serrated knife, slice the cake in half horizontally and place the bottom half on a cake stand or serving plate cut-side up. Spread with 1 cup of the whipped cream, stopping about 1/2 inch from the edge of the cake, then top with the strawberry-rhubarb mixture. Place the second half of the cake cut-side dow, over the strawberry-rhubarb filling and spread the remaining whipped cream over top, going close to the edge of the cake. Garnish with the remaining sliced strawberries.
Cook's Note: To make this cake ahead, you can fully assemble and chill up to 4 hours ahead of time without the sliced strawberry and sugar garnish. Top with the sliced strawberries before serving.
Recipe courtesy Food Network Kitchens