Heat 2 teaspoons of canola oil in a small skillet over medium heat. Add the finely chopped onion and cook, stirring frequently, until softened, which should take about 6 to 8 minutes. Set aside to cool completely.
In a large mixing bowl, combine the cooled onion, ground turkey, dried cranberries (or other dried berries), chopped parsley, beaten egg, minced sage, thyme leaves, lemon zest, kosher salt, ground black pepper, and allspice. Mix gently to avoid overworking the ingredients. Cover the bowl and refrigerate the mixture for at least 1 hour or overnight to allow the flavors to meld.
Once the mixture is chilled, divide it into 12 equal portions and shape each one into a patty approximately 2 1/2 inches wide and 1/2 inch thick.
Heat 2 tablespoons of canola oil in a large nonstick skillet over medium-low heat. Place the patties in the skillet, ensuring they are not touching (you may need to cook them in batches). Cook the patties until they are golden brown on both sides and cooked through, with no pink remaining in the center. This should take about 3 to 4 minutes per side.
Serve the turkey-cranberry sausages immediately. If you need to keep them warm, place them in a 200°F oven for up to 30 minutes.