Begin by preheating the oven to 350 degrees F. Prepare two baking sheets with either parchment paper or a silicone baking mat.

In a suitably sized mixing bowl, cream 1/2 cup butter until it achieves a smooth consistency. Ensure the sides of the bowl are scraped during this process.

Proceed by incorporating 3/4 cup granulated sugar and 1/4 cup brown sugar into the mixture. It is paramount to ensure a fluffy texture without any residual butter lumps.

Introduce 1 cup of peanut butter to the mixture. Ensure a homogeneous blend.

Subsequently, add the egg and vanilla extract to the mixture and mix until fully integrated.

Without stirring, add 1 and 1/2 cups of all-purpose flour to the bowl. On top of this, sprinkle the baking soda and kosher salt. Before mixing with the wet ingredients, combine these dry ingredients slightly.

Using a mixer, gently incorporate the dry ingredients into the wet mixture. It is imperative to avoid over-mixing. Once a rough dough forms, with some flour still visible, pause to scrape the sides and bottom of the bowl. Continue until the dough is uniform, but refrain from overworking it to maintain cookie tenderness.

Form the dough into balls of approximately 1 and 1/2 inches in diameter.

Arrange the formed dough on the prepared baking sheets, ensuring adequate spacing between each piece to allow for spreading.

Employ a fork, periodically dipped in sugar or flour to prevent sticking, to press a criss-cross pattern onto each cookie, flattening them to an approximate thickness of 1/2 inch.

In a separate vessel, smooth out 1/2 cup of seedless jam to remove any lumps. With precision, place up to 1 teaspoon of this jam at the center of each cookie, ensuring it remains centralized and does not reach the edges.

Bake the prepared cookies in the preheated oven for a duration of approximately 13-15 minutes. It is critical to observe for a slight browning along the edges, indicating their completion.

Once baked, it is advised to let the cookies solidify on their respective baking sheets for a duration of 5-10 minutes prior to transferring them onto a cooling rack.

For those prioritizing aesthetics, one may opt to enhance the cookies' appearance by adorning them with additional jam, melted peanut butter, and a sprinkle of chopped peanuts.

This procedure yields approximately 28 cookies. Store any excess in an airtight container, where they will remain optimal for consumption for up to three days.

Note: The cookie dough exhibits excellent freezing properties. For those inclined to prepare ahead, one can form the dough, flatten it using the aforementioned fork technique, and subsequently freeze it. This enables direct baking from the freezer, requiring only a minor adjustment in baking time. If one desires, the jam can be added prior to freezing, but ensure a preliminary flash freeze on a baking sheet before transferring to a freezer bag for longer-term storage.