Place squid in a small bowl; add enough milk to cover. Let soak, refrigerated, for at least 2 hours or up to 1 day.
Bring a large pot of salted water to a boil. Prepare an ice-water bath. Add fennel; cook until tender, about 5 minutes. Using a slotted spoon, transfer to ice bath; drain, and set aside.
Preheat oven to 325 degrees. In a small saucepan, bring shellfish broth to a simmer over medium heat; reduce by half.
Meanwhile, drain squid on paper towels; season with salt and pepper. Heat 1/8 inch olive oil in a medium ovenproof skillet over medium heat; add fennel, garlic, and thyme. When oil begins to sizzle, transfer pan to oven. Add tomato confit after 2 minutes.
Lightly coat a large skillet with canola oil; set over medium-high heat. Season both sides of the fish with salt; season the flesh side with pepper. Add fish to pan, skin-side down, reducing heat to medium-low; weight fillets briefly with another skillet to prevent curling. Remove skillet, and cook until skin is golden and crisp, 4 to 5 minutes. Using a spatula, turn over fish and cook for 1 minute; drain on paper towels.
Bring shellfish broth to a simmer; add squid, and simmer until bodies begin to curl, about 1 minute. Stir in parsley; remove from heat.
Remove pan from oven; drain fennel and tomatoes on paper towels.
Divide fish among 4 serving plates, centering them skin-side up; arrange fennel, tomatoes, and squid around fish. Pour one-quarter broth around each serving. Serve immediately.