In a skillet, melt 2 tablespoons of butter over medium heat. Add the lobster meat and sauté for 2-3 minutes until just cooked. Remove the lobster and set aside.

Make the Cognac Sauce

In the same skillet, add the remaining butter and shallots. Sauté until the shallots are translucent. Add the cognac and cook for another minute to reduce slightly.

Combine Cream and Egg Yolks

In a bowl, whisk together the heavy cream and egg yolks until smooth. Slowly add this mixture to the skillet, stirring constantly to avoid scrambling the eggs.

Add Seasoning

Stir in the tarragon, salt, and pepper. Cook on low heat until the sauce thickens, about 3-5 minutes.

Finish with Lobster

Add the cooked lobster meat back into the skillet and stir to coat with the sauce. Heat through for another minute.

Prepare the Toast

Toast the brioche slices until golden brown. If using gluten-free bread, ensure it is toasted properly.

Serve

Spoon the lobster mixture over the toasted brioche and serve immediately.