Bring a large pan of water to the boil, tip in the greens and cook for 1 min, then drain and leave in the colander to cool a little.
Melt 1 tbsp butter with the oil in a large pan. Add the leeks and a big pinch of salt, then stir over a medium heat until softened, about 8 mins. Add the garlic and cook for another min, then remove from the heat, tip into a large bowl and leave to cool.
Squeeze as much water out of the greens as you can; if you don’t mind getting a tea towel dirty, the best way to do this is to pile them onto the clean towel, gather the corners and squeeze. Add the greens to the pan with the leeks, then stir in the herbs, nutmeg, cheeses, eggs, zest and seasoning. Heat oven to 200C/180C fan/gas 6.
You’ll need a 23cm springform cake tin to assemble the tart in. Melt the remaining butter in a pan or the microwave and use some of it to grease the tin. Now you’re ready to work with the filo. Have a clean tea towel to hand to keep the sheets covered as you work (it can dry out very quickly). Layer the sheets of filo in the tin, brushing each one really well with butter and leaving plenty of pastry hanging over the edge, to close the top with once filled. Scatter the sesame seeds between each layer of pastry as you go. Save a few sheets for the top. Once the tin is lined, fill with the greens mixture. Scrunch a few more sheets of buttery pastry on top and fold in the overhanging sheets to close the tart. Scatter any remaining sesame seeds on top and drizzle over the remaining butter.
Bake for 40-45 mins until deep golden brown (cover with foil if it starts to brown too much). Remove from the tin as soon as you can to help keep the pastry crisp. Serve warm or cold.