Preheat the oven to 350°F (180°C).
Lightly grease cookie sheets or line with parchment paper.
Beat ¾ cup unsalted butter in a large mixing bowl until smooth, about 20 seconds. Gradually add 1 cup light brown sugar and ½ cup white sugar and beat for 2 minutes, until creamy, scraping the sides of the bowl as needed.
Add 1 egg and beat at medium speed for 3 minutes, scraping the sides of the bowl a few times. Add 2 tablespoons whole milk and 1 teaspoon vanilla extract or paste, mix until well incorporated.
Add 1 ¼ cups all-purpose flour, ½ teaspoon baking soda (sifted to avoid lumps), and ¼ teaspoon salt to the butter mixture. Mix at low speed until well blended, and no dry spots remain. But don't overbeat at this point.
Mix 3 cups old-fashioned rolled oats in two parts, so they're easier to incorporate. I use a rubber spatula for this part. Make sure no flour remains in the bottom of the bowl. At this point, the cookie dough can be refrigerated for up to a day. See note below.
Scoop out portions onto the prepared baking sheet, leaving space between them, an inch or two depending on the size of the cookie. If making larger cookies I flatten them slightly with my fingers tips so there's less chance of the center taking too long to bake and the sides being too brown.
Bake for 10-12 minutes, depending on the size, until golden brown and still soft in the center. I use a 1.5-inch cookie scoop and bake them for exactly 10 minutes.
Smack the pan on the counter immediately after you take it out of the oven. It will deflate the cookies a little and help with the texture.
Let cool on a wire rack before lifting them carefully from the paper and cooling them completely.
Once they cooled down completely, transfer the cookies to jars or an airtight container.