Remove one dough log from fridge. Slice into 1/4-inch thick slices (you should get 15 slices).
Transfer to one of the baking sheets, spacing 1 1/2-inches apart and bake in preheated oven until set, about 10 to 13 minutes.
Remove and let cool on baking sheet 5 minutes, then transfer to a wire rack to cool completely. Leave parchment paper on baking sheet for later.
Repeat slicing and baking process with remaining dough log from fridge.
Divide chocolate evenly among two small mixing bowls. Melt one batch in the microwave on 50% power in 30 second increments, stirring between intervals, until melted and smooth.
Place white chocolate in a third mixing bowl. Melt in microwave in 30 second increments, stirring between each, until melted and smooth. Transfer white chocolate to a piping bag with a small #4 round tip.
Dip cookies in chocolate (I work with about 4 cookies at a time to decorate so it doesn't set before finishing the web decoration), turn and let excess chocolate run back into bowl then transfer back to baking sheets that are lined with the parchment paper (dipped side facing upright).
Then right away do a dot in the center of the cookie with the white chocolate, followed by a piping of 3 rings around it all spaced evenly apart (refer to photos for a guide), or instead just do a spiral starting at the center of the cookie. Using a toothpick pull from dot at center to edge, repeat to create a web pattern (pulling to about 1/2-inch increments at edge).
Repeat this process with all of the cookies, and melting the second batch of chocolate. If the white chocolate hardens cover the tip with your fingertip and run under warm water facing it downward (dry bag exterior with paper towel so it doesn't drip on cookies).
Let chocolate set at room temperature or in the fridge to speed it up.