Make the ice cream: Heat the heavy cream, milk, honey, 1/4 cup granulated sugar, the lavender and a pinch of salt in a saucepan over medium heat, stirring occasionally, until hot but not boiling, about 5 minutes.
Whisk the egg yolks in a medium bowl; slowly drizzle in 1 cup of the hot cream mixture, whisking constantly. Gradually stir the hot egg mixture into the saucepan with the remaining cream mixture. Cook over medium heat, stirring constantly with a wooden spoon, until the custard is slightly thickened and coats the back of the spoon, about 8 minutes. Strain through a fine-mesh sieve into a bowl; discard the lavender. Fill a large bowl halfway with ice water. Carefully place the bowl of custard in the ice water and let sit, stirring the custard occasionally and adding more ice to the water as needed, until the custard is cold, about 30 minutes.
Meanwhile, preheat the oven to 375 degrees F. Generously coat a 9-inch pie plate with cooking spray. Pulse the graham crackers, the remaining 1 heaping tablespoon granulated sugar and 1/4 teaspoon salt in a food processor until finely ground. Transfer to a bowl and stir in the melted butter. Press the crumb mixture into the bottom and up the side of the prepared pie plate. Bake until lightly browned and set, 10 to 12 minutes. Transfer to a rack; let cool completely.
Freeze the custard in an ice cream maker according to the manufacturer's instructions, until it's the consistency of soft-serve. Spread in the cooled crust and sprinkle coarse sugar around the edge. Freeze until firm, at least 4 hours.