Make sauce: Combine raw cashews, 3/4 cup water, lemon juice, cumin, and salt in a blender and blend until smooth. Transfer to a container, cover and refrigerate until ready to serve.
Make burgers: Toast millet in 2 batches in a large, dry skillet over medium heat, stirring regularly, for 3 to 5 minutes. (Millet should smell nutty when done.) Transfer toasted millet to a bowl before adding second batch. Combine millet and 2 1/2 cups water in a pot and bring to a boil. Reduce heat to a simmer, cover, and cook until millet is tender and even in color, 15 to 20 minutes. Toward end of cooking time, add a pinch of salt. Let cool. Combine flaxseeds and 3 Tbsp. water in a small bowl; let stand until mixture forms a gel, about 10 minutes. Mix well. Combine carrot, scallions, basil, lemon zest, lemon juice, salt, and pepper in a large bowl. Once millet is cool, add it to bowl along with flaxseed mixture and mix well. Using your hands, shape mixture into 6 burgers.
Heat oil in a large skillet over medium heat. Cook burgers until golden brown, 7 to 8 minutes per side. Serve warm over lettuce leaves with a dollop of mango salsa and a drizzle of Cumin Cashew Cream Sauce on top. Uncooked burgers will keep for up to 4 days in refrigerator or 1 month in freezer, stored between pieces of parchment in a sealed container.