In a 6-qt. dutch oven, heat 2 tbsp. EVOO over medium heat. Working in batches, add the pork, season with salt and pepper and brown on all sides, about 5 minutes per batch; transfer to a bowl. Pour off the fat.
Add the onion, garlic, oregano, anchovies and remaining 1 tbsp. EVOO to the pan and season with salt and pepper. Cover and cook over low heat, stirring occasionally, until softened, 8 to 10 minutes. Add 2 cups water and bring to a boil over medium-high heat, stirring to scrape up any browned bits from the bottom of the pan. Add the pork, Fennel bulb and stewms and the apricots, season again and press a piece of parchment on top. Cover and cook over low heat until the meat is very tender, about 1 1/2 hours. Discard the fennel stems, ladle the stew into large, shallow bowls and garnish with the fennel fronds.