Use a mild flavored honey for this like wildflower or clover; the lighter the color - the milder flavor
Bring cream, half-and-half, honey, and lavender just to a boil in a 2 quart saucepan over moderate heat; stirring occasionally, then remove from heat. Let steep for 30 minutes.
Pour cream mixture through a fine sieve into a bowl and discard lavender. Return mixture to cleaned saucepan and heat again until just hot.
Whisk together eggs and salt in a large bowl, then add 1 cup of the hot mixture in a slow stream, whisking. Pour into remaining hot cream mixture in saucepan and cook over low heat, stirring constantly with a wooden spoon, until thick enough to coat back of spoon and it registers 170 to 175 degrees on instant read thermometer, about 5 minutes. Do not let boil!
Pour custard into cleaned bowl and cool completely, stirring occasionally. Chill, covered, until cold, at least 3 hours, but preferably overnight.
Freeze custard in ice cream maker. Transfer mixture into an air tight container and place in freezer to harden.