Add sage leaves, minced garlic, lemon juice and zest and hazelnuts to the bowl of a food processor.
Process until mixture forms a paste, then add oil and process until mixture is smooth.
Season pesto with salt and pepper to taste. Set mixture aside.
Place the half turkey breast in a large oven proof baking dish or on a rimmed baking sheet. With your fingers, carefully separate the skin from the turkey breast and spread sage pesto under the skin. Drizzle oil over the turkey breast, season with salt and pepper.
Roast the half turkey breast until a thermometer inserted into the center of the breast reaches 140 degrees (60 degrees C). That should take about 30 minutes.
Remove from pan, cover and let rest for 15 minutes. Slice turkey breast as needed, and drizzle with pan drippings if desired.
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