Combine the dried figs, water, honey, and lemon juice in a food processor. Pulse until the mixture is a thick, chunky paste.

Transfer the fig paste to a small bowl and stir in the vanilla extract. Let it cool completely at room temperature for at least 5 minutes.

In a mixing bowl, combine the softened butter and sugar, stirring for about 2 minutes until light and fluffy.

Beat in the egg and vanilla extract, stirring until smooth and well combined.

In a separate bowl, whisk together the flour, baking soda, and salt.

Add the dry ingredients to the wet ingredients alternately with the milk, starting and ending with the dry ingredients. Stir until just combined.

Divide the dough in half. On parchment paper, press one half into a rectangle about 1/4 inch thick and 2 inches wide.

Spread half of the fig filling down the center of the dough strip in a thin line, leaving about 1/2 inch on each end. Fold the edges of dough up and over the filling, sealing them together.

Repeat with the remaining dough and filling to create a second log.

Refrigerate the logs for 10 minutes.

Remove the logs from the refrigerator and carefully slice each into 12 equal pieces.

Preheat your oven to 350 degrees Fahrenheit. Arrange the sliced cookies on parchment-lined baking sheets.

Bake for 12 to 15 minutes, until lightly golden.

Let the cookies cool on the baking sheet for 5 minutes, then transfer them to a cooling rack.