Coat a wide, flat pan generously with olive oil. Bring the pan to a high heat and add the osso buco to the pan and brown them very well on all sides.
In a food processor puree the onion, celery, fennel, and garlic to a coarse paste. When the osso buco is well browned on all sides, remove from the pan and reserve. Ditch the excess oil from the pan and add a little new oil and bring to a high heat. Add the veggies to the pan with a pinch of crushed red pepper, season with salt, and brown them very well. Do not skimp on this step - it will take awhile, and that's ok. Add the tomato paste and cook until it starts to brown, 3 to 4 minutes. Add the wine and reduce by half.
Preheat the oven to 375 degrees F.
Return the osso buco to the pan. Add water so the liquid becomes even with top of the meat. Taste the liquid and season with salt if needed. Add in the bay leaves and thyme bundle. Bring the liquid to a boil, cover, and put the whole pan in the oven.
Cook the osso buco for 1 hour. Pull the pan out of the oven and check the liquid level and the seasoning. Add more liquid, if needed, return the pan to the oven, and cook for another hour.
Remove the lid and cook for 30 minutes. Remove the pan from the oven, remove the osso buco, and hold on a serving platter. Skim the fat off the surface of the sauce, if needed. Taste the sauce and adjust seasoning.
Remove the string from the osso buco. Serve the osso buco with sauce spooned over. Garnish with Gremolata. Serve with a demitasse spoon to scoop out the marrow.