Melt 1 1/2 tablespoons of butter in a saucepan over medium-high heat.

Add sliced mushrooms and chopped shallots to the saucepan and sauté for 3-5 minutes, until the mushrooms soften and release their juices.

Continue cooking, stirring frequently, for an additional 2-3 minutes, until most of the liquid is absorbed.

Stir in Cognac, chopped tarragon, salt, and pepper to taste.

Cook and stir for 1 minute, then let cool slightly.

Preheat a sandwich grill.

Melt the remaining 1 tablespoon of butter in a small saucepan over medium-high heat.

Place bread slices on a work surface and brush one side of each slice with the melted butter.

Turn the bread slices over and layer 1/4 of the Fontina cheese, half of the mushroom mixture, and half of the baby spinach leaves on the unbuttered side of two of the bread slices.

Divide the remaining cheese on top of the spinach.

Place the remaining two bread slices on top, buttered sides up, and press gently to pack.

Place the panini in the preheated grill, close the top plate, and cook for 3-5 minutes, until the bread is golden and toasted, the spinach is wilted, and the cheese is melted.

Serve immediately.