In a small heavy saucepan, combine 2 tablespoons of the sugar, 1 1/2 tablespoons of the lavender and 1 1/2 teaspoons of water. Cook over moderate heat, stirring constantly, until the sugar dissolves and the mixture forms a dry mass, 2 to 3 minutes. Transfer to a plate to cool, then grind to a fine powder in a spice grinder; set aside.

In a large heavy saucepan, combine the milk, creme fraiche, vanilla bean and remaining 1 1/4 cups sugar and 1/2 teaspoon lavender. Cook over moderate heat, stirring frequently, until the sugar dissolves and the mixture is hot, about 8 minutes. Remove from the heat, cover and let steep for 15 minutes. Strain the milk through a fine-mesh sieve and return to the saucepan.

In a large bowl, whisk the egg yolks until blended. Gradually whisk in one-third of the warmed milk mixture in a thin stream, then whisk the mixture back into the remaining milk in the saucepan. Stir in the reserved lavender powder.

Cook over moderately low heat, stirring constantly, until the custard lightly coats the back of a spoon, 5 to 7 minutes. Do not let boil.

Immediately remove from the heat and strain the custard into a medium bowl. Set the bowl in a large bowl of ice and water and let cool to room temperature, stirring occasionally. Cover and refrigerate until cold, at least 2 hours or overnight.

Pour the custard into an ice cream maker and freeze according to the manufacturer's instructions.