To make the cake: Preheat oven to 350 degrees F. Lightly oil a 9-inch round cake pan or coat it with nonstick cooking spray. Add breadcrumbs, tilting the pan to evenly coat the inside. Tap out excess.
In a small saucepan, melt butter over medium-low heat. Cook, swirling the pan, until the butter turns a nutty brown, about 30 seconds. Pour the butter into a small bowl. Whisk in oil, then buttermilk; set aside. Sift flour, baking powder and salt into a small bowl; set aside.
In a mixing bowl, combine eggs and sugar. Beat with an electric mixer on high speed until the mixture is thick and pale and falls in a ribbon when the beaters are lifted, about 5 minutes. Beat in vanilla.
Sift half of the reserved dry ingredients over the egg mixture; fold in with a rubber spatula until blended. Fold in half of the reserved buttermilk mixture. Repeat with remaining dry ingredients and buttermilk mixture.
Pour the batter into the prepared cake pan. Bake for 20 to 25 minutes, or until a skewer inserted in the center comes out clean. Let the cake cool in the pan on a wire rack for 5 minutes, then turn out of the pan and place right-side up on the rack to cool completely.
To make filling and syrup and assemble cake: In a bowl, whisk drained yogurt, mascarpone, confectioners' sugar and orange zest until smooth.
In a small saucepan over low heat, dissolve sugar in 1/2 cup water. Simmer gently for 5 minutes. Remove from the heat and stir in orange juice and liqueur.
With a long serrated knife, cut the cake horizontally into 2 layers using a gentle sawing motion. With a pastry brush, brush all of the syrup on the cut sides of the cake. Place the bottom layer on a cake plate, cut-side up. Spread half of the orange-mascarpone filling over the bottom layer. Arrange about one-third of the sliced strawberries in an even layer on top. Spread with the remaining filling. Place the second cake layer on top, cut-side down.
Brush the top of the cake lightly with about 2 tablespoons of the melted jelly. Arrange the remaining sliced strawberries in straight rows on top. Overlap the slices and reverse the direction of the slices in each row. Cover the cake with plastic wrap and place in the refrigerator to chill for at least 1 hour.
Just before serving, remelt the remaining currant jelly and brush it over the strawberries on top of the cake.