For anchovy and rosemary dressing, whisk ingredients in a bowl, season to taste, set aside.
Heat half the olive oil in a large frying pan over low heat, add onion and stir occasionally until very tender (15-20 minutes), add radicchio and frisée and stir until wilted (3-4 minutes). Add vinegar and reduce by half (1 minute). Season to taste and keep warm.
Heat remaining oil in a small frying pan over medium heat, add breadcrumbs and stir until golden (3-4 minutes), drain on absorbent paper and set aside.
Bring a large shallow saucepan of lightly salted water to just below the boil over high heat, reduce heat to low. Carefully break eggs into saucepan and poach, spooning water over eggs, until cooked to your liking (3 minutes for soft-poached). Gently remove with a slotted spoon, drain on absorbent paper and keep warm.
Divide braised greens between shallow serving bowls, top each with a poached egg, spoon over anchovy and rosemary dressing, scatter with breadcrumbs and serve hot.