In a large mixing bowl, use your finger tips to massage lemon zest into sugar until well combined. Add room temperature butter and brown sugar. Use a handheld mixer on medium speed to beat together sugar and butter until light and fluffy. Reduce speed to low and mix in milk and vanilla extract.

Add oats, flour, corn starch, cinnamon, baking soda, and salt. Combine on low speed until a soft dough forms. Cover and refrigerate for 15 minutes.

Preheat oven to 350°F. Line a large baking sheet with parchment paper. Use ~1.5 tbsp cookie scoop to distribute dough onto baking sheet. Bake for 14 minutes until light golden brown and crisp on the edges. The centers may seem underbaked, but that’s ok. It will continue to set while cooling. Cool on baking sheet for 10 min before transferring to a wire cooling rack.

Flip a cooled cookie over and place 1 generous scoop of strawberry ice cream on top. Use your scoop to gently spread the ice cream to the edges. Sandwich a cookie on top, then gently press together. Enjoy right away or immediately wrap assembled sandwiches in plastic wrap and freeze.

Freeze for up to 2-3 months.