Heat a sauté pan over medium heat with about 2 tbsp of butter. Clean and trim the leeks; you will only use the white and very light green parts. Slice them down the middle lengthwise, and slice into thin half-moons.
Sauté the leeks until softened and starting to brown, 7-10 minutes, adding a splash of water if they start to brown too much. Season with salt and pepper. Once cooked, spread them out on a plate and place them in the fridge to cool quickly.
In a large bowl, combine flour, salt, baking powder and sugar. Stir well to combine.
Use a box grater to shred the butter. Add the shredded butter to the flour mixture and use your fingers to distribute it well. Then add the shredded cheese and cooled leeks and toss to combine. Then add the heavy cream and egg yolk and mix until a shaggy dough is formed.
On a well floured surface, turn your dough out and squeeze it together into one mass of dough. Roll it out to an 8 inch circle, then cut into 8 evenly sized triangle slices. Line a baking sheet with parchment paper or a silicone mat and carefully arrange the scones on it, ensuring there is at least 1 inch of space between them. Place them in the fridge for 20 to 30 minutes.
While the scones are in the fridge, preheat your oven to 400.
Brush each scone with egg white and sprinkle with flaky salt. Bake until golden, 20-22 minutes.