To Cook The Beets: Wash and trim the beets. Peel and small dice them and place in a medium saucepan. Cover with heavily salted water and bring to a boil over high heat. Reduce heat to medium and gently boil until knife tender, about 30 to 40 minutes. Remove from heat and let cool in the water until able to be handled.

To Make The Beet Salsa: Transfer all but a few pieces of beet (save a few for garnish) to a blender, saving the water. Add 1 1/4 cups of the beet water, sesame seeds, garlic, lime juice, and salt. Blend on high until smooth, at least 1 minute. Sauce should easily run off the back of a spoon, add more beet water if necessary. Taste and add more salt as desired. Combine the queso fresco, mint, and cilantro in a medium bowl and set aside until ready to use.

To Make The Chilaquiles: Heat oil in a large frying pan over medium-high heat. Once shimmering add tortilla pieces, separating them as you add them to the pan (you may need to do this in 2 to 3 batches depending on the size of your pan — don’t overcrowd). Cook, stirring occasionally, until as evenly light golden brown as possible, about 2 to 3 minutes. Remove with tongs to a paper towel-lined baking sheet, sprinkle immediately with salt.

Remove any excess oil, reserving about 2 tablespoons in the pan. Return pan to medium heat and carefully add beet salsa to the hot oil, stirring constantly until sauce is boiling and cooked, about 2 minutes. Add tortillas back to the sauce, turning to coat. Remove from heat and cover.

Meanwhile, fry eggs to your desired doneness. Divide chilaquiles between the plates, top with an egg or two, the herbed cheese, and any or all garnishes you’d like. Serve immediately.