Heat olive oil in a large deep skillet, saute or paella pan over medium-high heat.
Place the whole fresh chorizo links in the skillet, reduce heat to medium and brown well on all sides.
Transfer to a plate and let cool to the touch. When cool enough to touch, slice the sausage into 1/4 to 1/3-inch thick slices. THE SAUSAGE WON'T BE COOKED ALL THE WAY THROUGH.
Refresh oil if needed. Add the onion and cook 3-4 minutes or until beginning to soften. Add the red bell pepper and tomato and continue cooking another 2-3 minutes.
Add the garlic, brown rice, Hungarian and smoked paprika, cayenne, saffron threads, salt and black pepper and give the rice a good stir to coat with the fat.
Place the sausage slices into the pan.
Carefully pour 5 cups of chicken broth into the pan. Bring to a boil.
Cover completely, reduce heat to low and simmer 45-50 minutes or until liquid is almost absorbed and rice is very close to tender. Adjust heat as necessary to keep it at a good simmer and stir at least twice.
At this point, there should still be a little bit of liquid in the pan. If not, add a little more chicken broth as you don't want the rice to get too dry. (A little crusty rice on the bottom is desirable.)
Add the shrimp and cook 5-6 minutes or until shrimp is pink and thoroughly cooked.
Stir in the peas and heat through. Cover and let rest for 5 minutes. Taste and adjust for seasoning.
Garnish with chopped fresh parsley and serve with lemon wedges.