Separate the white/light green parts of the leeks from the dark green tops.
Wash all parts thoroughly to remove grit.
Thinly slice the white and light green parts for the gratin. Reserve the dark green tops for frying.
Preheat the oven to 350°F.
Lightly butter a gratin dish.
Layer squash slices evenly, seasoning lightly with salt and white pepper.
Add a thin layer of sliced leeks.
Repeat layers until the dish is full, finishing with squash on top.
Pour cream over the gratin until it just reaches the top layer but does not fully submerge.
Cover tightly with foil. Bake 45–60 minutes until the squash is fully tender.
Remove the foil and bake an additional 15–25 minutes until lightly browned on top and the cream has reduced and thickened.
Let stand 15–20 minutes before serving to allow it to set.
Heat oil in a small saucepan to 325°F.
Add the sliced dark green leek tops in batches and fry until golden and crisp, about 1–2 minutes.
Transfer to a paper towel-lined plate. Season immediately with flaky salt.
Spoon warm gratin onto plates, add crème fraîche if using, top with cold caviar, and scatter crispy leeks over the top.