For the Mushrooms
Melt butter in a large sauté pan over medium-high heat. Add mushrooms and sauté until tender and almost all liquid has evaporated, about 5 minutes.
Add shallot, thyme and cook for 1 minute. Add brandy, stir, then add cream. Reduce cream for a minute or 2, until thickened slightly. Season to taste.
For the Rye French Toast
For Rye French toast, whisk eggs with milk. Heat a griddle over medium heat. Dip each slice of bread in egg mixture to coat. Grease griddle with butter and fry French toast, about 3 minutes on each side, until golden. Remove from griddle and keep warm.
To serve, cut each French toast slice in half and spoon mushrooms over. Serve immediately.