In a large saute pan, heat 1 Tbsp olive oil over over medium heat.
Add the shallot and saute for 2-3 minutes.
Add the mushrooms, salt, pepper, and thyme and saute for 5-7 minutes, or until the mushrooms are soft.
Add the wine and allow the liquids to reduce until there is very little excess liquid, about 10 minutes. Set aside.
Slice through the flank steak horizontally, but do not cut all the way through, in order to open it like a book. Place plastic wrap over it and flatten slightly with a meat mallet, heavy pan or rolling pin. Remove the plastic wrap.
Spread the mushroom mixture over the steak, about an inch from the edge, then scatter the crumbled blue cheese over the mushrooms.
Starting on one of the sides parallel to the grain, carefully roll the steak tightly, and tie in several places with butcher's twine.
In a bowl, whisk together all of the gravy ingredients except the thyme.
In a large dutch oven, heat 1 Tbsp olive oil over high heat and sear the braciole for 2-3 minutes on each side.
Once seared, pour the gravy over the braciole, add the sprigs of thyme, cover and bring to a boil.
Reduce to a simmer and braise for 1-1/2 hours.
When done, slice and serve with gravy.
Recipe by Cupcakes & Kale Chips at http://cupcakesandkalechips.com/2014/04/13/beef-wellington-braciole/