Cook the millet with a pinch of salt.. Set aside to cool.
While the millet is cooking, combine the flaxseeds and water in a small bowl; set aside until the mixture forms a gel, about 10 minutes. Then mix well.
Combine the carrots, scallions, basil, lemon juice, lemon zest, salt, and pepper in a large bowl. Once the millet is cool, add it to the bowl with the flaxseed-carrot mixture and mix well. Using your hands, shape the mixture into 6 burgers.
In a large skillet, heat the oil over medium heat. Place the burgers in the skillet and cook until golden brown, 7 to 8 minutes on each side.
To make the Mango Salsa: Combine of the ingredients in a large bowl; toss to combine. Add more red onion, if desired, for a spicier salsa.
To make the Cashew Cream Sauce: Combine all the ingredients in a blender and blend until smooth.
Serve burgers warm, wrapped in lettuce leaves with a dollop of the Mango Salsa and a drizzle of Cashew Cream Sauce on top. Uncooked burgers will keep for up to 4 days in the refrigerator or 1 month in the freezer, stored between pieces of parchment paper in a sealed container.