Preheat the oven to 350 degrees.
Heat a large skillet over medium heat. Add one tablespoon of the oil, and cook the chorizo for a few minutes until it's lightly browned. Remove the chorizo from the pan and put it in a large mixing bowl.
Add the kale to the pan, along with another tablespoon of the oil. Cook the kale until it is very dry and then add it to the mixing bowl.
In a second, smaller skillet, melt 2 tablespoon of butter and cook the minced onion until it is soft and slightly browned.
While the onion cooks, add the Manchego, eggs, salt, pepper and thyme to the mixing bowl.
When the onion is cooked add it to the bowl, too.
Melt the rest of the butter. Brush one sheet of the phyllo with butter and lay it on the bottom of the pie pan. Repeat with 11 more pieces of phyllo. Cover with the filling and then top with 12 more pieces of buttered phyllo.
Bake for 40 minutes, until the pie is golden brown. Garnish with thyme and pepper.