Preheat oven to 400 F. Wrap beets in foil, roast 45-55 minutes. Cool, peel, blend with lemon juice. Strain. Measure 1 cup puree.
Reduce oven to 350 F. Grease pans, line with parchment, grease parchment.
Whisk flour, cornstarch, cocoa powder, baking powder, baking soda, salt. Set aside.
Beat butter 2 minutes. Add sugar and beat 3-4 minutes until pale and fluffy.
Add eggs one at a time. Add vanilla and beet puree. Mix on low.
Add flour mixture in 3 additions, alternating with buttermilk in 2 additions. Mix on low.
Stir vinegar and oil together. Fold into batter with spatula. Do not overmix.
Divide between pans. Bake 28-33 minutes until toothpick shows moist crumbs.
Cool in pans 10 minutes. Cool completely on wire rack.
For frosting: beat cream cheese and butter until smooth. Add powdered sugar cup by cup. Add vanilla and salt. Beat on medium 1-2 minutes.
Level layers. Frost, stack, crumb coat, refrigerate 20 minutes, apply final frosting.