Preheat the oven to 350°F (175°C). Line two large baking sheets with parchment paper or silicone baking mats. Position the oven racks in the center and lower-third if you will bake two sheets at once.

Cream butter and sugars

In a large mixing bowl or the bowl of a stand mixer fitted with the paddle attachment, beat the softened butter, granulated sugar, and light brown sugar together on medium speed until pale, fluffy and well combined, about 2 to 3 minutes. Scrape the bowl as needed.

Add egg and vanilla

Add the large egg and vanilla extract to the creamed butter and sugars. Beat on medium-low until incorporated, about 30 seconds. Scrape the bowl.

Combine dry ingredients

In a separate medium bowl whisk together the all-purpose flour, baking soda, and fine sea salt until evenly distributed.

Mix dry into wet

With the mixer on low speed, add the dry ingredients to the butter mixture in two additions, mixing just until no streaks of flour remain. Avoid overmixing to keep cookies tender.

Add oats, chips and nuts

Fold in the rolled oats (if using), semisweet chocolate chips, and chopped nuts with a spatula until evenly distributed. The dough will be thick and slightly sticky.

Scoop jumbo portions

Using a large ice cream scoop or a 1/3 to 1/2-cup measure, portion the dough into very large mounds (jumbo cookies) spaced about 3 inches apart on the prepared baking sheets. For uniform jumbo cookies, shape each mound into a slightly flattened ball — about 1/3 to 1/2 cup dough each yields 8–10 jumbo cookies per batch depending on exact size.

Baking and Finishing

Bake

Bake one sheet at a time in the preheated 350°F (175°C) oven for 12 to 16 minutes, or until the edges are golden brown and the centers look set but still soft. If baking two sheets simultaneously, rotate sheets front-to-back and switch rack positions halfway through; add 1–2 minutes to baking time if needed.

Rest on sheet

Remove the baking sheet from the oven and immediately sprinkle each cookie with a small pinch of coarse sea salt. Let the cookies cool on the baking sheet for 8 to 10 minutes — this allows them to finish baking gently and hold their jumbo shape.

Transfer to rack

Using a wide spatula, transfer the cookies to a wire cooling rack to cool completely. If desired, sift a light dusting of powdered sugar over cooled cookies for presentation.

Storage

Store completely cooled jumbo cookies in an airtight container at room temperature for up to 4 days. To keep them soft, place a slice of bread in the container; to freeze, arrange cooled cookies in a single layer on a tray, freeze until firm, then transfer to a resealable freezer bag for up to 3 months.