Preheat your oven to 350°F (175°C). Grease a 9x13-inch baking dish or line it with parchment paper for easier cleanup.

In a large bowl, beat the softened cream cheese with 1 cup sugar until smooth and slightly fluffy. Add the eggs one at a time, beating well after each. Mix in the vanilla and sour cream (or Greek yogurt) until smooth. Fold in the drained crushed pineapple, then set this mixture aside.

In another bowl, whisk together flour, baking powder, salt, and the remaining 2 tablespoons sugar. Add the cold butter cubes and use a pastry cutter, two forks, or your fingers to cut the butter into the dry mix until it resembles coarse crumbs. Stir in the milk until a soft batter forms.

Spread the cream cheese and pineapple mixture evenly into the prepared baking dish. Spoon the cobbler batter over the top in dollops, spreading carefully to cover as much of the surface as possible.

Bake for 40–50 minutes, until the top is golden and a toothpick inserted into the center comes out mostly clean.

Let the cobbler cool at least 20 minutes to firm up slightly. Serve warm or at room temperature.