This for me is the ultimate egg dish for brunch in bed à deux. If you are disinclined to spring for the caviar you should provide some other salty counterpoint to the sweet, butter-poached lobster.

A layer of oven-crisped paper thin pancetta tucked between lobster and brioche will do in a pinch.

Make ahead:

1. Combine the vinegar with about 10 cups (2.5 L) of cold water, bring to the boil and remove from the heat.
2. Add the lobster and cover. Steep for 1 minute.
3. Remove lobster from pot, break off its claws, and return them to the pot for another 3 minutes.
4. Twist the tail from the body, remove the tail meat from its shell, clean, rinse and set aside to drain on paper towels.
5. Remove meat from claws and knuckles. Cover lobster meat and refrigerate until needed.
6. Reserve carcass and shells for another purpose.
7. If the lobster is female, transfer egg sacs to a small baking sheet lined with parchment paper and cook in an over preheated to 350°F for about 5 minutes–until eggs are red and firm. Set them aside to cool.

Prepare the beurre monté:

1. Heat a deep saucepan on medium, add 1 Tbsp (15 mL) of water, and then incorporate the butter one cube at a time, allowing each to emulsify completely before adding another.
2. Keep warm, maintaining a temperature between 160°F and 180°F (70-83°C) so as to preserve the emulsion.

Prepare the hollandaise:

1. In a stainless steel mixing bowl thoroughly whisk together the egg yolks and 1 Tbsp (15 mL) of cold water.
2. Place bowl over a pot of barely simmering water and continue to whisk until the mixture thickens and the whisk leaves behind streaks in the mixture.
3. Then begin whisking the butter one cube at a time.
4. Add lemon juice to taste, adjust seasonings and keep warm.

To finish:

1. For the eggs, bring water and vinegar to a boil in a sauté pan.
2. Cut lobster into but sized pieces and add to the beurre monté, submerging it completely.
3. Swiftly add shelled eggs one at a time to the vinegared water and poach for 3 minutes.
4. Toast the broche (and butter if desired).
5. Remove eggs to drain on paper towels.
6. Divide toasted brioche between two warmed plates.
7. Use a slotted spoon to remove lobster from the butter and arrange it on the four slices of toast.
8. Top each mound off lobster with a poached egg, a generous spoonful of hollandaise.
9. If you have cooked lobster roe, grate it over the eggs with a micro plane.
10. Finish each egg with a large quenelle of caviar and a sprinkling of chive.

Enjoy at once.