Season each piece of the tuna on both sides with the salt and pepper. Heat a grill to high and grill the tuna to the desired temperature.
Serve the tuna with the asparagus and tomato sauce.
Preheat the grill to medium.
In a shallow baking dish, toss the asparagus with the oil to coat well. Add the salt, and pepper and toss.
Place the asparagus on the grill in a single layer, and cook, turning, until marked and tender, about 12 to 15 minutes. Transfer to a platter, sprinkle with the lemon juice and drizzle with olive oil, to taste. Cover with aluminum foil and let sit for 5 minutes before serving.
Preheat the oven to 400 degrees F.
In a large, 14-inch, oven proof frying pan, combine all of the ingredients. Stir to blend then transfer to the oven and cook until the tomatoes begin to caramelize, about 30 minutes. Remove the skillet from the oven and stir well. Return to the oven and continue to cook until further caramelized and much of the liquid has evaporated, about 30 minutes longer. Serve immediately. (Alternately, cool slightly, and transfer to a blender, in batches if necessary, and process sauce until coarsely pureed. If the sauce seems too thick, thin with a bit of water or chicken broth.)
To store, cool completely and refrigerate for up to 4 days in a nonreactive, airtight container.
The sauce is great on pasta as well as pizza and even makes a great dipping sauce for hors d'oeuvres. If you prefer a less rustic sauce, puree completely as described above and strain.
Large asparagus can be placed directly on the grill; smaller ones may fall through during cooking. If cooking thin asparagus, use a grill basket. If Romanita tomatoes are unavailable, use a combination of Roma and grape tomatoes to approximate the sweetness of Romanitas, or use another type of sweet tomato, such as Amorosa.
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