Instructions

Adjust oven rack to middle position and heat oven to 350 degrees. Grease three 8-inch round cake pans, line with parchment paper, grease parchment, and flour pans.

for the rhubarb

Using vegetable peeler, peel 1 ribbon from each side of each rhubarb stalk. Toss ribbons and ¼ cup sugar together in bowl. Slice remaining peeled rhubarb thin (you should have 4 cups) and toss with ¼ cup sugar in second bowl.
Arrange half of rhubarb ribbons in 1 prepared pan in neat single layer to cover entire pan bottom, cutting edges to fit. Arrange remaining ribbons over top, perpendicular to first ribbon layer, cutting edges to fit. Arrange 1 cup sliced rhubarb in even layer in each of remaining 2 pans.
Combine remaining 2 cups sliced rhubarb and remaining ½ cup sugar in medium saucepan and bring to boil over medium-high heat. Cook until tender, about 2 minutes. Using immersion blender, process rhubarb mixture until smooth, about 30 seconds; let cool completely.

for the cake

Whisk flour, 1¼ cups sugar, baking powder, baking soda, and salt together in large bowl. Whisk buttermilk, egg yolks, melted butter, oil, and vanilla together in separate bowl. Add buttermilk mixture to flour mixture and whisk until just combined.
Using stand mixer fitted with whisk attachment, whip egg whites and cream of tartar on medium-low speed until foamy, about 1 minute. Increase speed to medium-high and whip whites to soft, billowy mounds, about 1 minute. Gradually add remaining ¼ cup sugar and whip until glossy, stiff peaks form, 2 to 3 minutes.
Whisk one-third of whites into batter. Using rubber spatula, gently fold remaining whites into batter until no white streaks remain.
Distribute cake batter evenly among pans, smooth tops, and gently tap pans on counter to release air bubbles. Bake until tops are light golden and toothpick inserted in center comes out clean, 22 to 25 minutes, rotating pans halfway through baking. Let cakes cool in pans for 15 minutes. Remove cakes from pans, discard parchment, and let cakes cool completely on wire rack, about 2 hours.

for the frosting

Using stand mixer fitted with whisk attachment, whip butter, salt, and cooled rhubarb mixture on medium-low speed until combined. Slowly add sugar and continue to mix until smooth, about 2 minutes longer. Increase speed to medium-high and whip frosting until light and fluffy, about 5 minutes.
Reserve cake with rhubarb ribbons for top layer. Place 1 cake layer, rhubarb side up, on cake plate and spread 1 cup frosting evenly over top, right to edge of cake. Repeat with second cake layer and 1 cup frosting. Top with ribbon cake. Frost sides of cake with thin layer of frosting, about ¾ cup. Using basketweave pastry tip, pipe remaining frosting in horizontal bands around sides of cake. Serve.