Pat dry the steaks with a paper towel then rub with salt and pepper on both sides.
Heat the oil in a large skillet over medium-high heat. Add steaks with plenty of space in between, or cook in batches.
Allow the filets to cook undisturbed for 2-4 minutes per side (for medium-rare), or cook to your liking.
Once the steak is done, set aside on a plate and cover to keep warm.
To the same preheated pan add the remaining oil. Sautee the onions for 2-3 minutes. Add in the mushrooms and garlic and continue to cook stirring frequently for 3-4 minutes.
Stir in the broth and thyme; allow it to bubble until liquid is reduced by half, 5-7 minutes.
In a small bowl whisk well the almond milk and cornstarch.
Add the cornstarch mixture to the pan and whisk until sauce thickens, 2-3 minutes. Stir in the balsamic vinegar.
Return the beef to the pan and spoon over the sauce, keeping it on the heat for 1-2 minutes, more, or until just heated through.
Garnish with fresh thyme and serve immediately.