In a medium bowl, combine the yeast with 1/2 cup of the warm water and let stand until foamy, about 5 minutes. Stir in the sugar and 3/4 cup of the flour to form a sponge; cover and let stand until billowy, about 30 minutes.

In a large bowl, combine the remaining 2 cups of flour with the Gouda, walnuts and salt. Make a well in the center and add the yeast mixture and the remaining 1/4 cup plus 2 tablespoons water; add the butter and stir until a dough is formed.

Line a baking sheet with parchment paper. Scrape the dough onto a lightly floured work surface and knead until smooth, about 5 minutes; divide into thirds. Roll each piece of dough into a 12-inch log about 1 1/2 inches thick. Arrange the logs on the prepared baking sheet 2 inches apart. Loosely cover with lightly moistened paper towels and plastic wrap. Let stand for about 45 minutes, until risen.

Preheat the oven to 350°. Remove the plastic wrap and paper towels and bake the logs for about 35 minutes, until they are golden and puffed and an instant-read thermometer inserted in the center registers 205°. Let the logs cool on the baking sheet for 20 minutes.

Reduce the oven temperature to 300° and position 2 racks in the lower and upper thirds of the oven. Transfer the logs to a work surface. Using a serrated knife, slice the logs crosswise 1/3 inch thick. Arrange the slices cut side up on 2 baking sheets and bake for 45 minutes to 1 hour, until golden and crisp; flip the biscotti halfway through and shift the baking sheets from top to bottom and front to back. Transfer the biscotti to a rack and let cool completely before serving.