For the Ice Cream:

1. Combine the egg yolks with the sugar in a large bowl. Using a whisk or a handheld mixer, beat the yolks and sugar for a few minutes or until fluffy and lightened in color.
2. Meanwhile, heat the milk and salt in a medium saucepan. Bring to a simmer.
3. Slowly stream the warm milk into the egg yolks while constantly whisking/beating at low speed.
4. Once all the milk has been incorporated, pour the entire mixture back into the same saucepan and place over low heat.
5. Stirring constantly, cook the custard until it is thick enough to coat the back of a spoon. Be careful to not let the custard come up to a boil.
6. Place a fine-mesh strainer over the same bowl used to beat the egg yolks and sugar together. Pour the hot custard through the strainer and into the bowl. Remove the strainer and whisk in the mascarpone, lemon juice, and vanilla. Let stand until cooled to room temperature, stirring occasionally, about 30 minutes.
7. Pour the custard into an ice cream maker and freeze according to the manufacturer’s instructions. Transfer the ice cream to an airtight container and freeze until firm, at least 2 hours.

For the Cookies:

1. Preheat the oven to 375°F and line a large baking sheet with parchment paper.
2. Whisk together the flour, baking soda, and salt in a mixing bowl.
3. Meanwhile, in the bowl of a stand mixer, cream together the butter and sugars until light and fluffy, about 3 minutes.
4. Add in the vanilla extract and the eggs and beat to thoroughly combine.
5. Slowly add in the dry ingredients, beating until the ingredients are combined.
6. Stir in the chocolate chunks by hand.
7. Scoop out the cookie dough onto the prepared baking sheet, leaving a couple inches between them. Sprinkle each cookie dough ball with some flaky sea salt.
8. Bake for 11-13 minutes, or until golden and crisp around the edges. Allow the cookies to cool on the baking sheet for a couple minutes and then transfer them to cooling racks to finish cooling completely.

To Assemble:

1. Once the cookies are completely cool and the ice cream has set in the freezer, line a large baking sheet with parchment paper and take the ice cream out of the freezer to soften slightly for a few minutes.
2. Scoop roughly ¼ cup of ice cream onto the flat side of one cookie and then top with a second cookie, gently sandwiching the softened ice cream between the two cookies. Set the formed ice cream cookie sandwich on the baking sheet. Continue with the remaining ingredients.
3. Once all the sandwiches have been formed, place the baking sheet in the freeze to allow the ice cream to set again. Freeze for at least 30 minutes before serving.