Preheat the oven to 400 degrees F and line a baking sheet with foil. In a large bowl, toss the strawberries with 1/4 cup of sugar until evenly coated. Spread on the baking sheet and roast for 15-20 minutes, gently flipping and stirring the strawberries every 5 minutes. Allow to cool briefly, then transfer the berries and roasting liquid back into the same bowl (Note: don’t wait too long or the roasting liquid will solidify onto the foil). Use an immersion blender to puree (a standard blender or food processor can also be used).
In a medium bowl, vigorously whisk together the egg yolks and remaining 1/2 cup sugar.
In a medium saucepan, combine the half-and-half, clotted cream and vanilla extract over medium-high heat. Stir the ingredients as they heat up to help thin out the clotted cream.
Once the mixture starts to simmer, turn the heat to low. Quickly re-whisk the yolks, then ladle in the cream while whisking. Pour the mixture back into the saucepan, scraping the bowl with a spatula. Stir the mixture over low heat for several minutes until it thickens slightly and coats the back of the spatula. Stir in the pureed strawberries along with the orange liqueur, if using. (Note: adding a bit of alcohol improves the texture of ice cream by lowering its freezing point).
Pour the mixture into a medium-sized container (a quart-sized liquid measuring cup is a perfect option), and press plastic film directly against the surface to prevent a skin from forming. Chill until very cold, preferably overnight.
Prepare in an ice cream maker according to manufacturer's instructions.
Mascarpone cheese is a good substitution option if you can't locate clotted cream. Crème fraîche would also work.