Place a 15 to 17-inch paella pan over medium-high heat.
Add olive oil.
Season chicken, rabbit and duck with 1 teaspoon salt and black pepper.
Add meats to pan in a single layer.
Cook, turning occasionally, until deeply browned on all sides.
Move browned meats toward edges of pan.
Add green beans to center of pan.
Cook until beans begin to blister and soften.
Add garrofón beans and cook briefly.
Add grated tomato to center of pan.
Cook until tomato thickens and darkens slightly.
Stir in sweet Spanish paprika and saffron.
Immediately add water.
Stir gently to loosen browned bits from bottom of pan.
Add remaining 1/2 teaspoon salt and rosemary sprig.
Bring liquid to a strong simmer.
Simmer 25 to 30 minutes, until meats are tender and liquid is well flavored.
Remove rosemary sprig.
Add snails if using.
Taste liquid and adjust salt if needed.
Sprinkle rice evenly across pan in a thin layer.
Gently level rice with a spoon, but do not stir after this point.
Cook over medium-high heat 8 minutes.
Reduce heat to medium-low.
Cook 10 to 12 minutes, until rice is nearly tender and liquid is mostly absorbed.
Increase heat to medium-high for 1 to 2 minutes to form socarrat on bottom of pan.
Listen for a gentle crackling sound, but do not let rice burn.
Remove pan from heat.
Cover loosely with a clean kitchen towel.
Let paella rest 5 to 10 minutes.
Serve directly from the pan with a wooden spoon if desired.