Preheat the oven to 350°F. Pat the bison shanks dry with a paper towel. Season both sides with salt and pepper and dust with the flour.
Place a Dutch oven on the stovetop over high heat and add the olive oil and butter to the pan
When the oil and butter is hot, add the shanks and brown all sides, about 3 minutes per side.
Remove the browned shanks and set aside.
Reduce the heat to medium-high and add the onions, carrots, and celery to the pot. Season with salt and pepper and sauté until slightly tender, about 4 to 5 minutes.
Add the wine and deglaze the pan, scraping the delicious bits from the bottom of the pan.
Add the garlic, diced tomatoes, beef bone broth, thyme, oregano, basil, bay leaf, and jalapeno, then bring to a boil.
Return the shanks to the pan. If needed, add more beef bone broth to fully cover the shanks.
Cover with a lid and place in the oven for 2 to 3 hours, until the meat is falling off the bone. You can also leave it on a low simmer on the stove, but it’s better when you finish it in the oven.
Check the oven every 30 minutes, basting the shanks, and turn the shanks halfway through.
To serve, remove the shanks with a slotted spoon and place them on individual plates. Spoon the sauce from the pot over the shanks and garnish with parsley, Parmesan, and a lemon wedge.