Butter the stale bread and toast in the oven.
Chop the onion and carrot into cubes.
Fry off the lardons in a pan. Add the finely chopped shallots, mushrooms (blanched) and the onion and carrot. Sprinkle with flour, cook for 5 min, pour in half of the wine. Reduce by half.
Adjust the seasoning and incorporate 70g butter in small pieces, stirring continuously. Leave the sauce to keep warm in a bain-marie.
Pour the other half of the wine into a saucepan. Add 250 ml (834 fl oz, 1 cup) of water, the bay and the thyme. Boil for 5 minutes and skim. Lower the heat to a simmer.
Poach the eggs in this liquid and drain once cooked.
On a deep plate, put the eggs onto the warm toast. Cover with the wine sauce and serve immediately.