Preparation

1. For the squash: Preheat oven to 177°C (350°F) with a rack in the upper third. Cut the tops off the squash about 2 cm (¾ inch) down to make lids. Using a soup spoon, remove and discard the stringy pulp and seeds in the squash. Put a double layer of foil on a rimmed baking sheet, and rub with about 15 ml (1 tablespoon) oil. Place each squash cut side down on the sheet, and place its lid cut side down beside it. Roast until the squash are tender inside when probed with a knife tip, but not collapsed, 35-45 minutes; be careful not to overcook. While the squash are roasting, prepare the filling.

2. For the filling: Measure the amount of water needed for cooking the lobster as follows. Put the live lobster into a pot and fill with water to cover. Using tongs, remove the lobster and set aside in a large bowl. Bring the water to a boil, add lobster, cover, and turn off heat. After 4 minutes, return lobster to the bowl, remove claws and knuckles, and return them to the hot water in the pot. Allow to rest in the hot water for another 4 minutes, then add to the bowl and allow to cool until they can be handled. Use scissors to cut open the tail and remove the meat, placing it in a bowl. Crack open the claws and add claw meat to the tail meat. Cut the tail and claw meat into pieces the same size as the bay (small) scallops; set aside at room temperature. Use the lobster body for another purpose.

3. Bring a small pot of water to a boil. Add the tomatoes and boil for 10-12 seconds. Run under cool water and rub off the peels. Place a fine strainer over a small bowl. Halve and core the tomatoes, and over the strainer, gently squeeze out the seeds and any juices. Discard the seeds in the strainer. Chop the tomato into pieces the size of the scallops, and add to the juices in the bowl along with a pinch of salt.

4. In a medium saucepan over medium-low heat, melt 15 ml (1 tablespoon) of the butter and add the chopped onion. Stir to soften but not brown, 1-2 minutes. Add tomato, minced tarragon, and a couple of grinds of black pepper. Stir and simmer over low heat until the tomato juices have evaporated and the mixture is thick. Remove from heat and set aside.

5. In a large skillet over medium-low heat, melt another 30 ml (2 tablespoons) of the butter. Increase heat to medium-high and add the bay scallops, tossing until they take on a bit of color but are not opaque. Transfer the mixture to a bowl and return the pan to medium-high heat. Add the sea scallops and shallots and toss for 30 seconds. Add wine and boil for 1 minute; be careful not to overcook the scallops. Using a slotted spoon, transfer the mixture to the bowl of bay scallops. Press down on the mixture gently to collect the juices at the bottom of the bowl, then pour the juices back into the skillet. 

6. Reduce the liquid in the skillet until only about 30 ml (2 tablespoons) remain; if more juices collect in the bowl of scallops, add them to the skillet. Add the cream and simmer until reduced by half and the sauce coats the back of a spoon. Add the reserved tomato, scallops, and lobster. Stir gently so as not to break up the tomato or seafood. When the mixture is well heated, stir in parsley. Fill the squash with the mixture, top with lids, and serve hot.