Trim tips of zucchini and carefully slice each in half lengthwise. Using a sharp knife and then a spoon, carefully cut a 1 to 1 1/2 inch-wide hollow in the center of each. Sprinkle zucchini boats with a pinch of sea salt and set aside while you prepare the other ingredients.
Dice any thick pieces of leftover zucchini and reserve for filling, then dice up enough pattypan or summer squash to make 1 cup total.
Preheat oven to 375° F. Set out a deep baking dish large enough to accommodate the zucchini boats.
Place a large skillet over medium-high heat. Swirl the neutral oil in the hot pan and then add the lamb. Take care not to crowd the lamb—work in batches if necessary. Sprinkling with sea salt as you go, cook each side until nicely seared, 1 to 2 minutes. Remove cooked lamb and any accumulated juices to a bowl and set aside.
With heat still on medium-high, add the sherry vinegar and scrape up any brown bits. Next, add the olive oil, followed by the onions, garlic, and peppers. Cook, stirring often, until onions are translucent and the peppers are tender, 7 to 10 minutes. Toss in the za'atar, stirring until incorporated. Stir in reserved zucchini and the tomatoes, followed by the cooked lamb (with any juices), cooked brown rice, and finally, the corn kernels. Off heat and set mixture aside until cool enough to handle.
Spoon filling into prepared zucchini boats, pressing the filling in and mounding just a bit in the center. Pour about 1 1/4 cups water into the baking dish (the water helps to steam the zucchini boats as they bake), then carefully arrange stuffed zucchini in the dish. Carefully slide into oven, and bake for 40 minutes. Slide dish out, sprinkle Asiago over top, and bake just until the cheese is melted.
Pull baking dish from oven; carefully lift zucchini out of the dish—there may be hot water leftover. Arrange on a platter and serve right away.