• Preheat the oven to 275°F
• Season the pork shanks generously with salt and pepper.  In a deep 6 or 8-quart Dutch oven or similar heavy-bottomed pot, heat 2 tablespoons of oil over medium-high heat.  Add 2 of the pork shanks, turning so they brown on all sides.  Transfer to a plate, and repeat with the remaining pork shanks.  This will take approximately 10 minutes.  
• Reduce the heat to medium and add the remaining oil and the chopped fennel, onions and carrots. Cook, stirring frequently, until the vegetables are soft, about 5 minutes.  Stir in the garlic and cook for another 30 seconds until the garlic is fragrant. 
• Pour in the white wine and bring to a boil, simmer for about 2 minutes to reduce the wine.  Add the beef broth, fennel fronds, chopped sage, rosemary, sprigs of thyme, salt, pepper and the bay leaves. 
• Snuggle the braised pork shanks into the mixture until they are three-quarters submerged.  Add additional broth if necessary but do not totally cover the shanks with liquid.  
• Cover the pot and transfer to the lower third of the oven.  Braise the pork shanks for 2-½ hours.  Check the level of the liquid after 1-1/2 hours.  If the liquid in the pot is covering the shanks less than half way, add additional broth and return to the oven and cook until the pork is very tender when pierced with a fork.
• Remove the pot from the oven and transfer the pork shanks to a plate.  Cover the plate with foil to keep warm while making the gravy.

For the Gravy:

• Strain the cooking liquids through a fine mesh strainer set over a bowl, pressing down on the vegetables with the back of a spoon. Discard the solids left in the strainer, spoon off and discard as much of the fat as possible from the surface of the strained cooking liquids.
• Melt the butter in a small skillet set over medium heat and stir in the flour and cook the roux for 2 minutes.  While whisking continuously, slowly pour in the hot, strained cooking liquids and whisk until the gravy is thickened.  Transfer the gravy to a pitcher or dish.
• Serve with a mound of mashed potatoes in each of four shallow bowls and add a pork shank to each serving.  Pour a portion of gravy over the pork shanks and garnish with fennel fronds.