Heat grill to medium-high heat. Peel the thick outer layer from the fennel bulbs, slice the stalks off of the bulbs, slice the bulbs in halves and reserve all in acidulated ice water (ice water with 1 Tbsp of lemon juice). When ready to grill, remove the fennel from the water and pat dry. Reserve the water. Lightly toss in a bowl with 2 tsp of the olive oil and black pepper. Place the fennel on the hottest part of the grill and allow the fennel to smoke for approximately 1 minute. Turn and cook for an additional 30 seconds. Remove the fennel and quickly plunge into the existing ice water to arrest cooking and refresh. Remove from the water, pat dry and toss in a bowl with the remaining lemon juice and olive oil. Season with salt and pepper to taste. Reserve.
In a blender, combine all ingredients except the olive oil, fennel frond and lemon zest. Blend until smooth. With the motor running slowly, incorporate olive oil to emulsify. To finish, pour the base into a non-reactive bowl and whisk in fennel frond and lemon zest. If preparing in advance, add the fennel frond and lemon zest when ready to serve. Salt and pepper to taste.
To serve, toss the grilled stalks, fronds and bulbs in the vinaigrette and distribute evenly between four plates. Garnish with fennel blossoms.