Bring large pot of salted water to boil. Blanch fingerling potatoes until tender, 8 to 10 minutes. Drain; slice evenly to about 1/8 inch. Reserve.
Melt 2 teaspoons of butter; rub over corn. Wrap in aluminum foil; roast in 400°F oven until tender, about 20 minutes. Cool about 10 minutes; cut kernels from ear; reserve.
In large, heavy-bottomed sauté pan over medium-high heat, sweat onion, peppers and shallots in 2 tablespoons butter until onions are translucent, about 3 minutes.
Add potatoes, shrimp, corn, herbs, cream, ground red pepper, salt and pepper. Reduce heat to low; simmer, stirring occasionally, until potatoes are tender and shrimp is cooked, about 6 minutes. Correct seasoning.
In medium sauté pan, cook quail eggs in butter sunny-side up until firm, about 2 minutes.
Per portion: Loosely mound home fries in center of small bowl or soup plate. Top with fried quail egg.