Place the strawberries in a pan with the honey and 80 g of the sugar. Bring to a rapid simmer, cook for 3 minutes then cool in a bowl over iced water.
Make a custard by bringing the cream and milk to a simmer. Whisk the yolks with the remaining 100 g sugar, then carefully whisk in half the hot cream. Pour it back into the still simmering cream mixture and turn the heat up to moderate. Cook until the custard coats the back of a spoon, stirring constantly and making sure it doesn’t boil. Strain through a fine sieve into a clean bowl and allow to cool down to body temperature. Stir in the cooled strawberry mixture then cover and place in the fridge for a few hours to chill down. Churn in an ice-cream machine or pour into a freezer-proof dish and freeze for an hour. Use a fork to break up the ice crystals as they form every hour, and keep freezing it, until you can stir no more.