In a saucepan, combine the heavy cream, whole milk, honey, sugar, salt and coarsely ground coffee. Heat over medium until steaming, do not boil.
Remove from heat, cover, and let steep for 20-30 minutes to infuse the coffee flavor.
Strain through a fine-mesh sieve, then through a layer of cheesecloth, pressing on the grounds to extract liquid. Discard the grounds.
Reheat the strained dairy over medium until steaming again. While it reheats, whisk the egg yolks.
Slowly pour about a cup of the hot dairy into the yolk mixture, whisking constantly to temper the eggs.
Pour the tempered yolk mixture back into the saucepan with the remaining dairy and the vanilla bean paste. Cook over medium-low, stirring constantly, until the custard thickens enough to coat the back of a spoon. Remove from the heat.
Whisk in the instant espresso powder until fully dissolved.
Strain the custard once more if needed, cover, and chill in the refrigerator until completely cold, at least 4 hours or overnight.
Churn in your ice cream maker according to manufacturer instructions until thick and soft-set.
Place into a freezer safe container until set, at least a few hours. Then top with honey and flaky sea salt if you’d like.
