In a saucepan, bring the half-and-half to a simmer.

Meanwhile, whisk the eggs and sugar together in a bowl until very well combined and thick.

When the half-and-half is simmering gently, scoop out about 1 cup of it and pour it slowly into the egg mixture, whisking the egg mixture constantly. When it's completely combined, pour it carefully into the saucepan with the remaining half-and-half and cook over medium-low until it thickens and coats the back of the spoon.

Remove from heat and stir in cinnamon and vanilla. Chill completely (at least a couple of hours).

Mix in your ice cream maker according to manufacturer instructions, crumbling half of the oatmeal cookies in while it churns.

Transfer to a resealable container, stir in the other half of the crumbled cookies and swirl in the caramel sauce. Freeze for a few hours before serving.