Melt 3 Tablespoons of clarified butter in large non-stick sauté pan over medium heat and add mushrooms.
Cook until mushrooms have softened and browned slightly, 3-4 minutes, shaking pan occasionally.
Remove from heat, set mushrooms aside but reserve pan. Drain A of potatoes, and spread in pan.
Season lightly with salt and pepper, and sauté for 3 minutes, or until lightly browned on bottom. Do not stir potatoes as they cook.
Flip galette and add a Tablespoon of butter, spreading around edges. Brown second side.
Slip out of pan onto sheet pan and repeat three times to make 4 galettes total.
Preheat oven to 325ºF. Place one galette on wire rack. Reserve 3/4 of mushrooms. Top with 3/4 of remaining mushrooms, then sprinkle with A green onions, 3/4 cheese. Layer three more times, ending with cheese. Bake 15 minutes. Remove from oven and cool slightly.
Heat grill or grill pan over high heat. Season medallions with salt and pepper. Place medallions on grill and sear 45 seconds to 1 minute, until one set of grill marks is seared onto medallions.
Lift medallions and rotate 90º, grill again 30 to 45 seconds to set criss-crossing grill marks. Flip and grill second side 1 minute. Move to cooler part of grill and cook 1 to 2 minutes more, depending on thickness of medallions and personal preference.
Reserve and keep warm. Veal can also be finished in 375ºF oven.
Heat clarified butter in medium sauté pan over medium heat.
Add shallots and cook until translucent or just starting to brown.
Add Calvados and deglaze pan, scraping up bits that have stuck to bottom.
Add thyme and cook until pan is almost dry. Add veal stock and reduce by one third, until slightly thickened.
Whisk in butter until sauce is smooth. Strain through fine sieve and adjust seasoning to taste.
Melt butter in medium sauté pan over medium heat. Add blanched baby vegetables and cook 2 to 3 minutes, until heated through.
Cut galette into 8 pieces with sharp serrated knife*. Place one slice galette at 2 o'clock position on each plate.
Place sautéed baby vegetables at 7 o'clock. Overlap two veal medallions at 5 o'clock. Drizzle reduction around entire plate.
Garnish with reserved mushrooms and fresh chives. Drizzle with a bit of olive oil.
Note: This recipe uses only 4 pieces of galette. Use remaining galette for another meal.