Heat oven to 425°F. Line a baking sheet with parchment.
Sauté leeks in olive oil over medium heat until tender, 4–5 minutes. Cool completely.
Whisk flour, baking powder, baking soda, salt, and pepper in a large bowl.
Cut in cold butter with a pastry cutter until pea-sized bits remain.
Fold in cooled leeks, cheddar, and chives to evenly distribute.
Pour in buttermilk and gently mix just until a shaggy dough forms.
Turn dough onto a lightly floured surface. Pat into a rectangle, fold in half, and pat to about 3/4-inch thick.
Cut biscuits with a 2–2.5 inch cutter, pressing straight down. Gather scraps and cut again.
Arrange on the sheet, touching for taller sides. Brush tops with cream.
Bake until golden and cooked through, 14–17 minutes. Cool 5 minutes before serving.