Preheat oven to 400°F (200°C).

Lightly grease 2 x 12-cup muffin pans.

Place pumpkin, oil, and rosemary in a baking dish.

Season to taste with salt and pepper.

Bake for 15-20 minutes, until the pumpkin is tender.

Meanwhile, for the pastry cases, cut 3-inch rounds from puff pastry using a cutter.

Press the pastry rounds into the prepared muffin cups.

Bake the pastry cases for 10-12 minutes, until golden brown.

For the filling, heat oil in a frying pan on high heat.

Cook chorizo and red onion for 4-5 minutes, until golden brown and the chorizo is cooked through.

Drain the chorizo and onion on a paper towel to remove excess grease.

In a bowl, combine the pumpkin mixture, chorizo and onion mixture, and chopped parsley.

Spoon the filling into the baked pastry cases.

Sprinkle the feta cheese over the tarts.

Serve the savory pumpkin and chorizo tarts immediately.