Preheat the oven to 425 degrees Fahrenheit. Trim any greens off the top of the beets, but leave amount 1/4 inch of them at the top so they beets don't dry out too much when roasting. Rub the outside of the beets with the olive oil. Add 1/2-inch of water to the bottom of small casserole dish, add beets, cover the pan with a lid or with tin foil, and roast in the oven until tender when poked with a fork (the exact cook time will vary depending on the size of the beets, for small beets it will be about 40 minutes, for large beets it may be closer to an hour).

Allow the beets to cool to where they are still very warm but safe enough to touch without burning yourself. The skin will just peel right off when you rub the beets with your fingers (you can wear food-safe gloves if you don't want your hands to stain super pink). Discard the skins, and chop the beets into eighths.

Put the peeled roasted beets in the blender with 1 egg and 1/2 cup of the cream and blend at high speed until absolutely silky smooth, about 2 minutes.

In the bowl of a stand mixer fitted with the paddle attachment, beat together the cream cheese and sugar at medium-low speed until combined and smooth. Increase the speed to medium and add the remaining eggs, one at a time, waiting until each egg is incorporated before adding the next one. Add the beet mixture, then add the remaining 1 1/2 cups cream, the vanilla, and the salt and beat until *just* combined. Sift the flour over the bowl and mix at low speed until it is just incorporated, about 20 seconds.

Bake at 400 degrees Fahrenheit until slightly burnt looking around the edges, but still slightly jiggly in the center, about 1 hour to 1 hour 10 minutes.

Allow the cheesecake to cool in the pan for 30 minutes (it will fall drastically as it cools, and that's okay!), the remove the side supports of the springform pan and allow to cool completely. Then carefully peel away the parchment paper from the side of the cheesecake. Slice and serve, or you can refrigerate it in an airtight container and enjoy it for up to 1 week.