Even though I may not use cornstarch next time, I'm going to give you the instructions so you can make it the way I did. It turned out well, so maybe the cornstarch was a good idea after all.
6.5ozgive or take--I'd say anywhere between 6 and 8 oz of cookies your favorite speculoos cookies (I used Archway)
28ozhalf and half, divided use
3ozby weight, dark brown sugar
2teaspoonscorn starch
ΒΌteaspoonkosher salt(or to taste)
For the Mix-Ins
Broken/Crumbled/Chopped Cookies, frozen (about 1 cup's worth) I had 3 windmill cookies left, so that's what I used
For the Swirl
3-4Tablespoonsdark brown sugar
Instructions
For the Ice Cream Base
Place the cookies in a large bowl.
Pour 20 oz half and half over the cookies, stir, and refrigerate for at least an hour or up to 4 hours.
Strain the "cookie milk" through a fine mesh strainer, tapping the side of the strainer firmly with a wooden spoon to keep it flowing and pressing down gently on the solids. Don't push down so hard that actual cookie goo is coming through. Towards the end, some thicker stuff will come through, but try to keep it at a minimum. Discard the cookies (feed them to a pet or something).
To the milk, add the dark brown sugar, salt and corn starch.
Whisk over medium high heat until the mixture reaches a boil and thickens. Let boil for maybe 10 seconds and then strain into a metal bowl set in an ice bath.
Chill, stirring occasionally, until cold.
Pour in the last 8 ounces of half and half. Taste for salt and adjust if necessary.
Churn in your ice cream maker according to manufacturer's instructions.
Putting It All Together
Add the cookies during the last 2-3 minutes of churning or just fold them in until evenly distributed.
Sprinkle about 1- 1 1/2 Tablespoons brown sugar in your container.
Layer in about 1/3 of the ice cream.
Sprinkle on more sugar, then ice cream, then sugar and finish with ice cream.
Press plastic wrap down directly on the surface of the ice cream and ripen in the freezer for at least 4 hours.