In a small bowl, whisk together the red wine vinegar, honey, garlic, thyme, red pepper flakes and liquid smoke. Set aside for 10 minutes to allow the flavors to develop (optional).
Place the bison flank steak in a shallow dish. Drizzle with olive oil and season with salt and pepper on both sides. Pour the marinade over the bison flank steak and let the steak marinate for an hour at room temperature; or chill and marinate overnight. Bring the steak to room temperature prior to cooking from chilled.
Meanwhile, in a small bowl, stir together the Greek yogurt, shallot, honey, lemon juice, oregano and dill. Cover and chill while cooking the steak.
Turn on the broiler to low and preheat oven for 10 minutes – if your oven doesn’t have high/low broil, place the oven rack about 5-6 inches from the broiler before turning it on.
Remove the steak from the marinade and discard the excess marinade. Place the steak on a baking sheet. Place the steak in the oven and cook for 6-8 minutes for rare (130 F), 8-10 minutes for medium rare (140 F), or 10-15 minutes for well-done (160 F).*
Let the steak rest for 5 minutes after taking it out of the oven. Slice the bison against the grain into long, thin strips.
While the oven is still hot and the bison flank steak is resting, turn off the broiler and warm the pita pockets for 3-4 minutes.
Assemble the pitas by stuffing the pockets with bison flank steak strips, spinach, onion, cucumber, tomato, feta cheese and homemade tzatziki sauce as desired. Enjoy!
*We recommend flank steak cooked rare for the most delicious results!