In a large bowl combine flour, baking powder, and salt. Whisk together.
Add sourdough discard, olive oil, and water, but do not mix. Set aside.
Heat 1 tbsp extra virgin olive oil in a Dutch oven or heavy pot with lid over medium heat. Crumble sausage into the pot and cook, stirring occasionally, until browned. Remove with a slotted spoon to a bowl.
Add onion and garlic to the pot and cook 5-6 minutes, stirring occasionally, or until onion is softened and starting to become translucent. Add broccoli and cook, stirring occasionally, until just starting to soften, about 1-2 minutes. Add sherry or wine, broth, heavy cream, cheese, ¼ tsp salt, and ¼ tsp pepper. Return sausage to the pot. Bring to a simmer, stirring occasionally.
Mix together wet and dry ingredients from steps 1 and 2 to form a batter. Drop dumpling batter by the rounded tablespoon (a cookie scoop works great for this, if you have one) into the pot. You should get about 10-12 dumplings. Cover pot, reduce heat to low, and cook until dumplings are fluffy and cooked through, about 20 minutes (to check, cut a dumpling in half to make to sure no raw dough remains).
Divide soup and dumplings into bowls. Top with fresh cracked black pepper if desired.