Custard: Put the cream and milk into a saucepan, bring just to the scalding point, and turn off heat. Scrape the seeds from the vanilla bean into the cream then drop in the pod and the anise-hyssop leaves. Let sit for thirty minutes. Pour through a strainer to remove the herb leaves and vanilla pod, pressing with a spatula to make sure no cream is left behind. Return the cream mixture to the saucepan along with two-thirds of the sugar, and reheat it to melt the sugar, but do not let it pass the scalding point. Remove from heat and keep hot, covered.

Beat together yolks, remaining sugar, and salt in a large bowl with an electric mixer at high speed until tripled in volume and thick enough to form a ribbon when the beater is lifted. This will take 3 to 4 minutes in a stand mixer, but longer with a handheld mixer.

Whisking constantly, slowly add the hot cream to the egg yolks. Transfer the custard back to the saucepan. Cook over moderately low heat, stirring constantly with a wooden spoon, until custard is slightly thickened and registers 170°F (do not let it boil!). Set aside to cool.

Peaches: Put the flower pieces into a spice grinder with the sugar, and process to a fine powder. Place the peaches into a saucepan along with the processed sugar and lemon juice, and stir to combine. Bring to a boil and cook, mostly covered but stirring often. After ten minutes, remove lid, reduce heat, and simmer for thirty minutes longer, stirring occasionally.

Cool the peaches a bit and then use a hand-held blender to somewhat puree them. Stir the peaches into the custard and refrigerate until well-chilled, at least two hours. Churn according to your ice-cream maker manufacturer's instructions.