Preheat the oven to 350°F (180°C). Line a large baking sheet with parchment paper.
Grate the zucchini using the small holes of a box grater. Place it in a clean kitchen towel and squeeze firmly to remove as much liquid as possible.
In a large bowl, whisk together the all-purpose flour, oats, baking powder and salt.
Add the cold butter.
Quickly work it into the flour using your fingertips or a pastry cutter until the mixture resembles coarse crumbs with some pea-sized pieces of butter remaining.
Add the squeezed zucchini, cheddar or a mix of cheeses.
Give everything a quick stir.
Pour in the cold buttermilk.
Gently mix just until the dough comes together. Do not overmix.
Transfer the dough to a lightly floured surface. Gently press it into a rectangle about 1 cm thick.
Fold the dough.
Fold it into thirds, like a letter.
Turn it and gently press it out again.
Repeat the folding process one more time. This creates the flaky layers.
Finally, gently press the dough to about 2 cm thick.
Cut out biscuits using a floured 6 cm round cutter or simply cut into squares. Press the cutter straight down without twisting.
Place the biscuits on the prepared baking sheet.
Brush the tops with beaten egg and sprinkle with cheddar and sesame seeds or everything bagel seasoning.
Bake for 20–25 minutes, or until puffed and golden brown.
Let them cool for a few minutes and serve warm.