Heat heavy cream, half-and-half, honey, and lavender flowers in a heavy 2-quart saucepan, stirring occasionally, until cream just starts to bubble. Remove from heat and cover; let steep for 30 minutes.
Strain cream mixture into a bowl using a fine-mesh sieve. Discard lavender flowers. Clean saucepan and pour strained cream mixture back in. Heat over medium heat until hot, about 5 minutes.
Whisk eggs and salt together in a bowl. Whisk in 1 cup hot cream in a slow stream.
Pour egg mixture into the remaining hot cream in the saucepan. Cook over medium-low heat, stirring constantly with a wooden spoon, until custard coats the back of the spoon and reads 175 degrees F (80 degrees C) on an instant-read thermometer, about 5 minutes.
Pour custard through a fine-mesh sieve into a bowl. Let cool completely, stirring occasionally, about 15 minutes. Chill, covered, for at least 3 hours.
Freeze custard in an ice cream maker according to manufacturer's instructions, about 20 minutes. Transfer to an airtight container and place in the freezer to firm up.