Preheat oven to 350 degrees F and lightly grease a 9x13-inch baking dish.
Add frozen strawberries directly to the prepared baking dish. Sprinkle cornstarch, lemon zest, lemon juice, vanilla extract, and salt over the top.
Toss everything together until the strawberries are evenly coated.
Remove cookie slices from package or if using a log of cookie dough, slice into ¼-inch to ⅓-inch rounds. Arrange the cookie dough pieces in a single layer over the strawberry mixture, leaving a little space between each so the filling can bubble up as it bakes.
Bake for 45-55 minutes, until the strawberry filling is bubbling around the edges and in between the cookie pieces and the cookie topping is baked through and turning golden. If desired, you can set your oven to broil for 1-2 minutes to deepen the color and crisp up the cookie topping. Watch closely as cookies can burn quickly.
Let the cobbler cool for at least 15-20 minutes before serving. The filling will thicken as it sits. Sprinkle on more lemon zest if desired.
Serve cobbler warm with ice cream.