Preheat the oven to 180°C (160°C fan / 350°F).
Take a 9 x 13-inch rimmed baking sheet and brush it with a bit of the olive oil.
Lay a sheet of filo onto the top half of the baking sheet and brush with olive oil. Place a second sheet of filo over the bottom half of the baking sheet, there should be some overlap in the middle. Brush with more olive oil.
Coninue with the layering until you have 2 sheets of pastry left. Rip them into random pieces about 3 inches wide and set aside.
Mix the ricotta with the pesto, lemon zest and thyme in a medium bowl. Stir in the egg until smooth. Spread this over the pastry, leaving 1 inch slight border of pastry uncovered around the edge.
Lay the broccoli over the ricotta in an even layer. Top with the crumbled feta and fold in the edges of the pastry.
Take the random shredded pieces of filo and crumple them up, place around the border of the tart.
Brush the whole tart with any remaining olive oil and sprinkle the edges with the sesame seeds.
Bake for 25-30 minutes until browned around the edges and the broccoli is starting to colour.
Remove from the oven and cut into 8 pieces. Serve hot.