How to Make It
In a large saucepan, combine the beets and potatoes. Add enough water to cover by 2 inches and bring to a boil over high heat. Cook until the beets and potatoes are tender, 35 to 40 minutes. Drain well. When cool enough to handle, peel the beets and potatoes, and then coarsely chop; transfer to a food processor. Add 2 tablespoons of the butter and puree until smooth. Season with salt and pepper and keep warm.
Heat a large cast-iron skillet. Rub the pork chops all over with 2 tablespoons of the olive oil; season with salt and pepper. Cook over moderately high heat until golden brown on the bottom, 7 to 8 minutes.Turn the chops and add the garlic, sage and 2 tablespoons of the butter. Cook until the chops are golden and an instant-read thermometer inserted in the thickest part registers 135°, about 7 minutes longer. Transfer the pork chops to plates and let stand for 5 minutes. Whisk the lemon juice and 2 tablespoons of the butter into the skillet; season with salt. Strain the sage butter through a fine sieve over the pork chops. Reserve the crispy sage leaves and discard the garlic.
Meanwhile, in a large nonstick skillet, melt the remaining 2 tablespoons of butter in the remaining 2 tablespoons of olive oil. Add the chard in large handfuls; let each batch wilt slightly before adding more. Cook, stirring occasionally, until all of the chard is wilted, 5 minutes. Season with salt and pepper.
Serve the pork chops with the beet puree and Swiss chard and garnish with the crispy sage leaves.