Step 1Place the canola oil, olive oil and garlic in a small skillet and gently heat on low for 3 to 4 minutes. Turn off the heat and let the garlic infuse the oil for 15 minutes for a subtle garlic flavor, longer for a stronger flavor. Remove and discard the garlic.
Step 2Bring a medium-sized saucepan of water to a boil. Fill a large bowl with ice and water. Blanch the basil leaves in the boiling water for 30 seconds, then drain and place in the ice water. Drain again and lay between sheets of paper towels; squeeze out as much of the liquid as possible. Place in a blender, along with the garlic-infused oil and salt. Puree until smooth.
Step 3Strain the oil through a fine-mesh strainer into a covered container. Refrigerate until ready to use. Gently shake the container before each use.
Step 1Whisk the vinegar, salt and pepper in a small bowl. Add the olive oil, whisking to emulsify.
Step 1Combine the white wine, chicken broth, lemon, garlic, parsley, salt and peppercorns in a fish poacher or large roasting pan. Bring to a boil, then reduce the heat and simmer for 15 minutes. Rinse the fish filets, place them in the hot liquid and poach for 5 minutes. Carefully lift them out with a spatula and place them on a platter. If serving chilled, cover and refrigerate.
Step 2Drizzle the basil-garlic oil on and around the fish. Drizzle the champagne vinaigrette over the basil oil. Garnish with chervil leaves.