1. For the Arepas, place milk, water and 1/4 cup (1/2 stick) of the butter in small saucepan. Cook on medium heat about 5 minutes or just until butter is melted. Remove from heat; cool slightly.
2. Combine masarepa and sea salt in medium bowl. Pour the milk mixture slowly into masarepa mixture, stirring until liquid is fully absorbed. (Mixture may be slightly lumpy.) Add feta and knead mixture with hands until smooth and cheese is fully incorporated. Divide dough evenly into 12 balls. Flatten each ball into a disk about 4-inches in diameter and 1/2-inch thick.
3. Melt 1 tablespoon of the remaining butter in large cast iron skillet on medium-high heat. Cook arepas in batches about 6 minutes per side or until golden brown and slightly crispy. Adjust heat to medium-low if arepas are browning too quickly. Add additional butter to skillet between batches if needed. Transfer arepas to a platter; cool slightly. (Arepas can be made up to 3 days ahead. Refrigerate in airtight container. When ready to serve, bring to room temperature before reheating in a hot, buttered skillet.)
4. For the Moussaka, heat oil in large skillet on medium-high heat. Add eggplant; cook about 5 minutes or until slightly golden and softened, stirring occasionally. Add onions and garlic; cook and stir about 2 minutes or until slightly softened.
5. Add lamb to skillet; cook about 3 minutes, stirring occasionally. Add spices; cook about 3 minutes or until the meat is no longer pink and spices are toasted. Add tomatoes and water. Bring to simmer; cook about 7 minutes or until the mixture is slightly thickened, stirring occasionally. (Moussaka can be made 3 days ahead. Cool before refrigerating. When ready to serve, simmer until heated through.)
6. To assemble arepas, slice each arepa crosswise about 2/3 of the way to make a pocket. Spoon about 1/3 cup Moussaka into each arepa and sprinkle with feta. Serve immediately.
Test Kitchen Tips:
Arepa dough is made with masarepa, a pre-cooked cornmeal. The cornmeal can be found in Latin markets, the Latin aisle of the supermarket or online stores. Do not use masa harina, which is used for preparing tamales.
Keep a bowl of cold water nearby when preparing the arepa dough. If your hands get too sticky while kneading and forming the arepas, wet them in the cold water and continue working dough.
All components of this dish can be made ahead. Store prepared arepas and Moussaka in separate airtight containers in refrigerator up to 3 days. To serve, reheat arepas in a hot, buttered skillet and simmer moussaka until heated through.