How to Make It
Preheat the oven to 350°. Line a 9-inch square baking dish with plastic wrap. Rub the beets lightly with olive oil and wrap individually in foil. Bake the beets for about 1 hour, or until tender when pierced with a fork. Let cool slightly.
Meanwhile, in a medium enameled cast-iron casserole or Dutch oven, whisk the grits with the milk, water and 1 teaspoon of salt. Bring to a boil over moderate heat, whisking constantly. Cover the grits and bake in the oven for about 50 minutes, stirring 3 or 4 times. The grits are done when they're tender and the liquid has been absorbed.
Whisk 6 tablespoons of the butter and the egg yolk into the grits. Season with pepper. Spoon the grits into the prepared baking dish and press a sheet of plastic wrap directly onto the surface. Refrigerate until firm, about 1 hour.
Peel the roasted beets and cut them into 1-inch pieces. Transfer the beet pieces to a large bowl.
In a medium skillet, heat 1 tablespoon of the olive oil until shimmering. Add the mushrooms and thyme sprig and season with salt and pepper. Cook over moderately high heat, stirring occasionally, until the liquid has evaporated and the mushrooms are lightly browned, about 8 minutes. Add the wine and the remaining 1/2 tablespoon of butter and cook, stirring, until evaporated, about 1 minute. Add the mushrooms to the beets. Discard the thyme sprig.
Wipe out the skillet. Add 2 tablespoons of the olive oil and heat until shimmering. Add the shallots and cook over moderate heat, stirring, until softened. Add the vinegar, sugar and a pinch of salt and cook until slightly reduced, about 3 minutes. Stir in 1/4 cup of the olive oil and add to the beets and mushrooms. Stir in the chives and season with salt and pepper.
7. Spread the rice flour on a plate. Turn the grits out onto a work surface; discard the plastic. Cut the grits in half, then cut each half into eight narrow 4 1/2-inch-long rectangles. Dust the grits with rice flour. Divide the remaining 1 cup plus 1 tablespoon of olive oil between 2 large nonstick skillets and heat until shimmering. Add the grit cakes and fry over moderately high heat until golden and crisp all over, about 8 minutes total. Drain on paper towels and season lightly with salt. Transfer the cakes to a platter and top with the sweet-and-sour beets and mushrooms. Garnish with the baby greens and serve.
Kahan favors the white grits made by Byrd Mill in Ashland, Virginia. They're available at byrdmill.com.