For the filling: Position a rack in the center of the oven and preheat to 375 degrees F. Whisk together the jam, cornstarch, sugar, lemon juice and 2 tablespoons water in a large bowl until well combined. Add the strawberries and toss gently to coat evenly. Transfer the mixture to a 2-quart baking or gratin dish, using a spatula or the back of a large spoon to gently pack the fruit into an even layer. Set aside.
For the topping: Pulse together the flour, 1/4 cup of the sugar, baking powder, and salt in a food processor. Add the butter and pulse until the mixture resembles coarse meal. Add 3/4 cup of the cream and the vanilla and pulse until the dough just starts to come together. Do not over mix.
Spread the dough evenly over the strawberries, drizzle with the remaining 2 tablespoons cream and sprinkle with the remaining 2 tablespoons sugar.
Place the cobbler on a baking sheet and bake until the topping is lightly browned and the fruit is bubbling, about 1 hour. Let the cobbler cool completely before serving, 2 to 3 hours. Serve with vanilla ice cream.
When measuring flour, we spoon it into a dry measuring cup and level off the excess. (Scooping directly from the bag compacts the flour, resulting in dry baked goods.)
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