Step 1 Preheat oven to 200C. Place 1 filo sheet on a clean work surface and brush with a little melted butter. Fold filo in half to make a square. Repeat with another filo sheet and a little melted butter to make another square, then place on top of the first filo square at a 45-degree angle. Continue layering with remaining filo and melted butter, turning each filo square at a 45-degree angle, to make a stack. Cover with a damp tea towel.
Step 2 Melt the extra butter in a large 20cm (base measurement) ovenproof frying pan over medium heat. Add the carrots and shake the pan to cover the base in an even layer. Add the cumin, coriander and paprika and cook, shaking the pan occasionally, for 1 min or until aromatic. Drizzle with honey and cook, shaking the pan, for 1-2 mins or until carrots are well coated in honey and spices. Season. Remove from heat.
Step 3 Place the filo stack over the carrots, folding in the edges to fit the pan. Bake for 15-20 mins or until the pastry is golden brown and crisp.
Step 4 Place a serving plate over the top of the pan and invert the tart onto the plate. Sprinkle with the fetta and serve immediately.