Step 1

In a small saucepan, combine the soy sauce, sake, lime juice, ginger and sugar and bring to a boil; stir to dissolve the sugar. Pour the marinade into a glass baking dish; let cool completely. Add the salmon, turn to coat and marinate for 1 to 4 hours, turning occasionally.

Step 2

Preheat the broiler. Broil the salmon, skin side down, 5 inches from the heat until golden, about 3 minutes. Turn the fillets and broil for 4 minutes, or until the skin is crisp and the fish is not quite cooked through. Transfer to a plate.

Step 3

In a medium saucepan of boiling water, cook the udon until heated through, 1 minute. Drain the noodles and transfer to soup bowls.

Step 4

Heat the olive oil in a large skillet. Add the spinach by handfuls and cook over high heat, tossing, until wilted. Mound the spinach on the udon and top with the salmon. Spoon the cooking juices in the baking dish over the fish, sprinkle with the sesame seeds and serve.