Make the custard base: In a medium saucepan, whisk 5 large egg yolks and 3/4 cup granulated sugar until the mixture is pale yellow. Add 3 cups whole milk, 2 teaspoons vanilla, and 1/4 teaspoon flaky sea salt.
Cook the custard: Set the saucepan over medium‑high heat and stir constantly. Bring to a low boil and continue stirring until the mixture thickens and coats the back of a wooden spoon, about 8–10 minutes. Remove from the heat immediately.
Strain and chill the custard: Pour the hot custard through a fine‑mesh sieve into a large heatproof bowl. Let cool slightly, cover, and refrigerate at least 4 hours or overnight until fully chilled.
Make the cookie‑dough mix‑ins: In a large bowl, beat together 1 stick (1/2 cup) salted butter, 1/3 cup light brown sugar, and 1/4 cup granulated sugar until combined and creamy. Add 1 pasteurized egg and 2 teaspoons vanilla; beat until combined. Add 1 3/4 cups all‑purpose flour and mix until incorporated. Stir in 1 cup mini semi‑sweet chocolate chips.
Freeze and chop the cookie dough: Spread the cookie dough in an even layer on a parchment‑lined baking sheet. Freeze until firm, about 20–30 minutes. Remove from the freezer and roughly chop into small, bite‑size pieces; keep frozen until needed.
Preheat the oven for the oatmeal cookies: Preheat the oven to 350°F (175°C). Line a baking sheet with parchment paper.
Make the oatmeal cookie dough: In a large bowl, combine 1 3/4 cups old‑fashioned oats, 1 cup all‑purpose flour, 1 cup packed light brown sugar, 1/2 teaspoon baking soda, and 1/2 teaspoon salt. Add 1/2 cup canola oil (or melted coconut oil), 1 large egg, and 2 teaspoons vanilla extract. Stir or beat until the dough is moist and combined (the dough will be somewhat crumbly). Fold in 1 cup semi‑sweet chocolate chips.
Shape the oatmeal cookies: Using your hands, gather about 1 tablespoon of dough, squeeze it firmly into a compact ball, and place it on the prepared baking sheet. Repeat with the remaining dough, spacing cookies about 1–2 inches apart.
Bake and cool the cookies: Bake the cookies 12–15 minutes, or until set and golden. Transfer to a wire rack and let cool completely.
Churn the ice cream: Remove the chilled custard from the fridge and churn in your ice cream maker according to the manufacturer’s instructions. During the last few minutes of churning, add the frozen cookie‑dough pieces so they are evenly distributed.
Assemble the ice cream sandwiches: Place one scoop of the churned ice cream onto the flat side of half the cooled oatmeal cookies. Top each with a second cookie and gently press to form a sandwich.
Freeze the assembled sandwiches: Arrange the sandwiches on a parchment‑lined baking sheet and freeze until firm, about 4–6 hours.
Serve: Remove sandwiches from the freezer 5–10 minutes before serving to soften slightly. Enjoy.