Preheat oven to 375°F. Butter an 8-inch cast iron skillet or small baking dish.
If making the whipped yogurt topping, place Greek yogurt, heavy whipping cream, and sugar in a small bowl. Beat with an electric mixer or whisk by hand until thickened and softly whipped. Refrigerate until ready to serve.
Remove the tops from the strawberries and cut them into quarters. Place them in a medium mixing bowl.
Add granulated sugar, cornstarch, and lemon juice to the strawberries. Toss until the strawberries are evenly coated and the cornstarch is no longer visible.
Transfer the strawberry mixture to the prepared skillet or baking dish and spread into an even layer.
In a small mixing bowl, stir together self-rising flour and granulated sugar.
Add heavy cream and stir until a sticky, cohesive biscuit dough forms. Do not overmix.
Use your fingers or a spoon to dollop the biscuit dough over the strawberries, leaving some open spaces so the filling can bubble up around the topping.
Sprinkle the biscuit topping with coarse sugar.
Bake at 375°F for 35 to 40 minutes, or until the strawberries are bubbling around the edges and the biscuit topping is golden brown and baked through.
If the filling is bubbling but the biscuits are not as brown as you would like, move the skillet to the top rack of the oven for about 5 minutes, or broil for 1 to 2 minutes. Watch carefully.
Let the cobbler cool for 10 to 15 minutes before serving. Serve warm with whipped yogurt topping, whipped cream, or vanilla ice cream.