Place the dried porcini mushrooms in a heatproof bowl and cover with 2 cups boiling water. Set aside.
Season the venison strips with salt and pepper, then melt the butter in a wide braising pan over medium heat. When the butter begins to foam, brown the venison in batches and remove to a plate or bowl as it is cooked.
Add the olive oil to the pan and sauté the mixed mushrooms until they brown and begin to crisp up on the edges. (Do this in batches, if necessary—if the pan is crowded, the dish will get watery.)
As the mushrooms cook, remove them to the plate or bowl with the venison.
When the mushrooms are cooked, add the shallot and garlic to the pan and sauté briefly until fragrant and beginning to brown.
Add the tomato paste and fry until it turns a lovely brick-red color. Deglaze the pan with the brandy—scraping up all the brown bits from the bottom.
Drain the dried porcini mushrooms and add the soaking liquid to the pan—saving the rehydrated mushrooms for another use (they’re great in an omelet!).
Return the venison and the sautéed mushrooms to the pan and simmer for 10 minutes until the sauce comes together.
Season to taste with salt and pepper, then add the crème fraîche and stir well. Continue cooking just to warm through.
Serve over buttered egg noodles.