Put the cream, milk, honey, salt, and dandelion petals in a medium saucepan. Warm it slowly over medium-low heat, stirring now and then, just until it barely simmers, then take it off the heat.
Cover the pot and let the petals steep for at least 30 minutes, and no more than 1 hour.
Pour the cream through a fine mesh strainer into a bowl or measuring cup, pressing on the petals. Rinse the saucepan in cool water, since a hot pan will scramble the egg yolks.
Put the egg yolks in the cooled pan. Whisk constantly while you pour in the warm cream in a thin stream.
Turn the heat to low and keep whisking until the custard coats the back of a spoon and reaches 175°F (79°C) on an instant-read thermometer, 3 to 5 minutes. Don't let it go above 180°F.
Pour the custard into a heatproof bowl, press plastic wrap or parchment onto the surface, and chill it in the fridge for at least 4 hours, or overnight.
Churn it in an ice cream maker the way the manufacturer says, usually 20 to 30 minutes. Move it to a freezer-safe container, press parchment onto the surface, and freeze it 2 to 3 hours to firm up.
Notes
Picking dandelions: Pick from unsprayed lawns or organic pastures, away from roadsides, on a sunny, dry morning after the dew has dried. Remove every bit of green from the petals. The milky sap in the green parts is bitter and can spoil the batch.Honey: Use a mild, light honey like clover, wildflower, or orange blossom. Dark honeys like buckwheat or manuka cover up the dandelion.Custard temperature: Cook the custard to 175°F (79°C), or until it coats the back of a spoon and holds a line when you run your finger through it. Don't let it go above 180°F, or the eggs will scramble.No ice cream maker: Freeze the cold custard in a freezer-safe container. Every 2 hours, take it out and beat it with a stand mixer paddle, or stir it really well by hand. Do that 3 or 4 times, then let it firm up.Dairy-free: Use the non-dairy ice cream recipe that works for you, and add the dandelion infusing step at the start. Coconut cream works well.Storage: Keeps 2 to 3 months in the freezer. Press parchment right onto the surface before you put the lid on, so ice crystals don't form.