In a large bowl, mix together the flour and salt. Add the cold butter cubes to the flour. Cut the butter into the flour using a pastry blender or your fingers until it looks like coarse crumbs with some pea-sized pieces of butter still visible. Slowly add the ice water, one tablespoon at a time, mixing gently until the dough just starts to come together.
Take the dough out of the bowl and put it on a lightly floured surface. Gently pat it into a rectangle shape. Wrap the dough tightly in plastic wrap. Put it in the refrigerator and let it chill for at least 30 minutes.
Take the chilled dough out of the fridge and put it back on your lightly floured surface. Roll the dough into a rectangle that's about 12 inches by 16 inches. Bring one short end of the rectangle to the center, and then fold the other short end over it. Wrap the dough up again and put it back in the refrigerator for another 30 minutes.
Repeat the rolling and folding process one more time. Take the chilled dough, roll it into a 12x16 inch rectangle, and fold it into thirds again. Wrap it up and chill in the fridge for 30 minutes.
After the final chilling, take the dough out and roll it out to about 1/8 inch thick. Cut the dough into squares or rectangles.
In a medium saucepan, put in the raspberries, sugar, lemon juice, and water. Turn the heat to medium and bring it to a simmer. Cook, stirring occasionally, until the raspberries have broken down and the sauce has thickened, about 10-15 minutes.
Turn on your oven and set it to 375°F (190°C). Line a baking sheet with parchment paper.
Place the cut dough pieces on the baking sheet. In a small bowl, whisk together the egg and milk. Brush the tops of each flakie with the egg wash. Bake for 15-20 minutes until golden brown and puffed up.
Let the Homemade Flakies With Raspberry Compote cool on the baking sheet for a few minutes before serving. Spoon the warm raspberry compote over the flakies and enjoy.