Preheat the oven to 180°C conventional oven/ 160°C fan-forced (350° Fahrenheit/Gas 4). Grease a round baking dish with butter (alternatively, line a baking dish with baking paper).
Melt the butter in a medium-sized frying pan over medium heat. Add the olive oil, red onion and potatoes. Cook, continuously stirring until the potatoes are golden and tender (approximately 8 minutes though will vary depending on the thickness of the potatoes). Set aside to cool slightly.
Meanwhile, place the broccolini in a small saucepan with cold water. Bring to the boil, uncovered, then cook for a further 4 minutes. Drain the broccolini. Refresh under cold water and set aside to cool slightly then stir into the onion and potato mixture.
Use a fork to lightly whisk the eggs and cream together in a bowl until combined. Stir in the rosemary and season well with salt and pepper to taste.
Arrange half of the potato and broccolini mixture on the base of the baking dish. Scatter half of the Provolone cheese and ham over the potato and broccolini. Arrange the remaining potato and broccolini mixture and a final scattering of Provolone cheese and ham on top. Pour the egg and cream mixture evenly over the frittata with potatoes and broccolini. Bake the frittata for 35 minutes.
Allow the baked frittata with potatoes and broccolini to cool for 5 minutes before serving – buon appetito.