Heat creams and sugar in a heavy 3 quart saucepan, until very hot but do NOT let it boil.
Remove about 1 cup of the hot cream and whisk it into the egg yolks (this is called "tempering"). Now, return egg yolk mixture to the saucepan, whisking it in and whisking constantly.
Heat until custard is 160 degrees F -OR- custard will coat the back of a spoon. This should take about 3-5 minutes after whisking in the yolks. Remove from heat and cool to room temperature--stirring now and then to prevent a thick skin from forming. You can just leave it be and remove the skin entirely. I prefer to prevent it from forming. Choice is yours.
Transfer custard to a covered container (I use a dollar store plastic pitcher for this) and refrigerate until thoroughly chilled.
Place strawberries in a small bowl and add the 3 tbs sugar, tossing to coat well. Cover and chill.
When ready to make ice cream, stir the fruit (including accumulated liquid), food coloring (if using) and custard together.
Follow directions of your ice cream maker to freeze. I use a Lello Gelato Jr. This is the machine with the compressor already in it so I don't have to freeze a bowl. In my machine, this recipe makes *2* batches as it makes 1 pint.