Place a grill pan over medium-high heat or preheat a gas or charcoal grill.
Whisk the oil, chopped basil, chives, chopped tarragon, salt and pepper in a small bowl to blend. Brush the salmon and pineapple slices with the herb mixture.
Cook the salmon until barely cooked through and still pink inside, about 4 minutes per side. Cook the pineapple until slightly charred, 3 to 4 minutes per side.
Transfer 1 pineapple slice to each plate and arrange a piece of salmon slightly overlapping it. Spoon 2 tablespoons of the Avocado Dressing over each piece of fish. Garnish with basil and tarragon sprigs and serve.
Combine the lemon juice, basil, chives, olive oil, tarragon, anchovy paste if using, salt, pepper, garlic and avocado in a food processor. Add 2 tablespoons of water and process until smooth. Cover the dressing and let stand for at least 15 minutes and up to 1 hour for the flavors to blend.
If using canned pineapple, make sure to blot it dry very well before grilling it.