I prefer using golden beets because their color and flavor are brighter than red ones. Use whatever you prefer; just wear gloves to protect from staining your hands. If you want to use precooked or store-bought beets, simply cook the garlic and shallots in the mixed oils in a skillet until caramelized, then pour the oil over the beets and cheese as in Step 3.
Heat the oven to 375 degrees. On a large rimmed baking sheet, combine the beets, garlic, shallots, olive oil and 2 tablespoons chile oil. Toss to combine, then spread out in an even layer and season with salt and pepper. Bake until tender and caramelized on the bottom and at the edges, 1 hour to 1 hour and 15 minutes.
While the beets bake, heat the remaining 1 tablespoon chile oil in a small skillet over medium heat. Add the almonds and coriander seeds and cook, tossing occasionally, until the almonds are toasted, 3 to 4 minutes. Transfer the nuts and seeds to a cutting board and roughly chop while warm. Season the mix with salt.
Arrange the feta slices on the bottom of a serving platter. Remove the beets from the oven and place them over the feta while still hot, making sure the oil and aromatics from the baking sheet are drizzled evenly over top as well. Sprinkle over the almond-coriander mix, followed by the mint leaves, and serve immediately.
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