Melt a knob of butter in a small pan and cook shallots until softened.
Combine mashed Stilton, remaining butter, chives, cooked shallots, salt, and pepper in a bowl.
Roll the butter mixture into a cylinder with cling film and chill for 30 minutes.
Season steaks with oil, salt, and pepper, then sear in a hot pan for 2 minutes per side.
Transfer seared steaks to a tray and refrigerate until they are cold.
Preheat oven to 220°C and bake steaks for 6 to 10 minutes depending on desired doneness.
Top each hot steak with a disc of Stilton butter and rest for 2 minutes before serving.