In a large mixing bowl, whisk together the all-purpose flour, baking powder, and salt until combined. Next, add the softened butter, blending until the mixture resembles coarse crumbs. Press this dough firmly into a greased 9x13-inch baking dish and bake in a preheated oven at 350°F (175°C) for 12-15 minutes, until the crust is lightly golden.

While the crust bakes, heat a skillet over medium heat and add a drizzle of oil or butter. Slice the onions thickly, then add them to the pan. Cook for about 10-15 minutes, stirring occasionally, until the onions are soft and golden brown. Once caramelized, remove the skillet from the heat and allow the onions to cool.

In a large bowl, combine the cream cheese, sour cream, and eggs, whisking until smooth. Gradually mix in the shredded cheddar cheese. Gently fold in the cooled caramelized onions.

Pour the cheese and onion filling evenly over the pre-baked crust. Spread it out with a spatula. Place the dish back into the oven and bake for an additional 25-30 minutes, until the filling is set and a golden top forms.

Once baked, remove the dish from the oven and let the squares cool for about 10 minutes. Cut into squares, serving them warm or at room temperature.