Heat oil in a large Dutch oven (or another thick-walled iron cooking pot with a tight fitting lid) over medium-high heat.
Add squash, potato, onion, salt, pepper and nutmeg to pan; sauté 3 minutes, stirring occasionally.
Stir in broth; bring to a boil. Reduce heat and simmer 20 minutes or until vegetables are tender, stirring occasionally.
Remove from heat; let stand 15 minutes or until cooled slightly.
Place half of potato mixture and 1 cup half-and-half in a blender; process until smooth. Pour into a serving bowl.
Repeat procedure with remaining potato mixture and half-and-half. Cover and keep warm.
Combine 1/2 cup oil and chives in clean, dry blender; process until smooth. Strain mixture through a sieve over a bowl; discard solids.
Drizzle about 1 tablespoon chive oil over each serving.