Cut potatoes in half lengthwise.
Dip in olive oil, salt. Put on a baking sheet and bake for 40 minutes at a temperature of 200 ° C, turning once after 20 minutes.
When the potatoes are cooked, season the fish. Heat the butter in a frying pan and fry the fish over high heat for 2 minutes on each side, until a pronounced golden color.
Transfer to a baking sheet and bake for 5 minutes.
Place all sauce ingredients, except oil, lemon and pepper, in a blender and whisk quickly, pour in olive oil, then season with lemon juice and pepper. Serve on the table.