Preheat your oven to 350°F (177°C) and line a baking sheet with parchment paper, or use a nonstick tray.

In a medium bowl, beat the softened butter with the brown sugar and granulated sugar until creamy.

Add the egg and mix briefly until blended, then stir in the vanilla.

Add the flour, baking soda, salt, cinnamon, and nutmeg, and mix just until a smooth dough forms.

Fold in the oats and raisins so they are evenly spread through the mixture.

Scoop the dough in about 2-tablespoon portions onto the prepared baking sheet.

Bake for 8 to 10 minutes, until the cookies are lightly golden around the edges.

Let the cookies rest on the tray for 1 minute, then transfer them to a wire rack to cool completely.

In another bowl, whisk together the sweetened condensed milk, vanilla, cinnamon, and half-and-half until smooth.

In a separate bowl, whip the heavy cream with a hand mixer or stand mixer until stiff peaks form, about 60 to 90 seconds.

Gently fold the condensed milk mixture into the whipped cream until fully combined and smooth.

Break the cooled cookies into small chunks, about 1 inch in size, and fold them into the ice cream base.

Spread the mixture into an 8 x 8-inch pan or a similar freezer-safe container.

Freeze uncovered for 3 to 5 hours, or overnight, until firm.

Cover leftovers with foil or plastic wrap and keep frozen for up to 3 weeks.