combine the spices
In a small bowl, stir to combine the spices: coriander, paprika powder, thyme, oregano, garlic powder, salt, and pepper. Place the pork shoulder on a large plate. Drizzle the meat with a tablespoon of olive oil. Rub the spices into the meat.
sear the meat
Place a large dutch oven pot over medium-high heat. Add canola oil and pork. Sear on all sides; it will take approximately 10 - 12 in total. Turn the meat from time to time using kitchen thongs. Preheat the oven to 160 °C / 320 °F. Pour wine into a saucepan, place over high heat, bring to a boil, and then cook for a minute for the alcohol to evaporate. Remove from the heat.
braise the pork shoulder
Transfer the meat from the dutch oven to a large plate. Discard the fat from the pot. Peel the onion and cut it into quarters. Peel the carrots and cut them into larger chunks. Cut the garlic head in half. Add the vegetables to the dutch oven along with the thyme, sage, and bay leaf. Place the seared meat on top. Pour in the water or broth and wine. Cover with a lid. Place in the preheated oven on the middle rack. Braise for 2 - 2 1/2 hours at 160 °C / 320 °F or until the meat is soft and juicy. Using a ladle, pour the braising juices over the meat three times during cooking.
bake the veggies for the sauce
Cut the tomatoes, pepper, and onion into quarters. Place on a baking sheet and place in the oven last 40 minutes before the meat is done.
leave the meat to rest
When the pork shoulder is done, remove it from the oven and transfer it to a large plate. Leave to rest for 10 - 15 minutes, then cut into slices and serve.
make the sauce and serve
After taking the meat out, transfer the vegetables to a high rack. Change the oven setting to low broil. Broil for 10 minutes. Transfer the vegetables to a blender (or use an immersion blender). Using a slotted spoon remove the vegetables from the dutch oven and add them to the blender. Don't add the whole garlic, just about two cloves. Discard the herbs. Using a blender, mix into a thick sauce. Add 120 ml (1/2 cup) of braising liquid and mix again until creamy and smooth. Season to taste with salt and pepper. Serve with the Braised Pork Shoulder.