How to Make It
Halve limes, and discard any seeds. Cut lime halves into quarters; cut each quarter in half. Place limes in a medium bowl, and sprinkle with 1/4 cup salt. Cover and let stand 4 hours. Rinse limes under cold water, and discard any salt or liquid left behind.
Place rinsed limes in a medium saucepan; add 1/4 cup lime juice, 1/4 cup water, and remaining 1/4 cup salt. Cook over low, stirring occasionally, until limes are completely tender and liquid has reduced by almost half, 35 to 45 minutes. Remove from heat, and transfer mixture to a sterile jar. Add remaining 1/4 cup lime juice, seal, and refrigerate 8 hours or overnight. (When ready to use limes, rinse lime pieces well under cold water, and cut as desired.) Preserved limes may be stored in refrigerator up to 1 month.
Preheat oven to 400°F. Place beets and garlic in a medium bowl. Add oil, pepper, and 1/2 teaspoon salt; toss to coat. Transfer to a baking sheet, and roast in preheated oven until tender, 35 to 45 minutes.
Whisk together 1 tablespoon chopped preserved lime, yogurt, and a pinch of salt in a small bowl; set aside.
Spread yogurt mixture on a serving plate. Place roasted beets in center with any leftover pan juices. Garnish with parsley and 1/2 teaspoon chopped preserved limes, if desired.