Steps:
- Make the cookies:
- Preheat oven to 350°F. Toast walnuts on a rimmed baking sheet, tossing halfway through, until golden brown, 7-10 minutes. Let cool.
- Pulse walnuts and whole wheat flour in a food processor until finely ground. Add all-purpose flour and salt and pulse to combine.
- Using your fingers, work thyme into granulated sugar in a small bowl until mixture starts to look moist and clump together. Using an electric mixer on medium-high speed, beat thyme sugar, butter, and powdered sugar in a large bowl until light and smooth, about 2 minutes. Reduce speed to low and gradually add dry ingredients and mix just until combined. Use a rubber spatula to mix in any remaining dry spots or flour at the bottom of the bowl.
- Transfer dough to a sheet of parchment paper and form into a 12" log. Firmly roll up log in parchment paper, then wrap tightly in plastic. Chill on a flat surface until firm, at least 4 hours.
- Preheat oven to 350°. Slice off both ends of log to make neat edges, then remove plastic and parchment. Slice dough into 1/4"-thick rounds and place on parchment-lined rimmed baking sheets, spacing about 1" apart. Bake, rotating baking sheets halfway through, until edges of cookies are light golden but centers are still pale, 10-15 minutes. Let cookies cool on baking sheets 5 minutes, then transfer to wire racks and let cool completely.
- Make the icing and assemble:
- Whisk powdered sugar, orange zest, orange juice, cream, coconut oil, thyme, and salt in a medium bowl until no lumps remain.
- Using a spoon or small offset spatula, spread about 1 tsp. icing over each cooled cookie (you will have some icing left over). Let cookies sit until icing is set, at least 45 minutes.
- Do Ahead
- Dough can be made 1 day ahead. Keep chilled, or freeze up to 1 month. Cookies can be frosted 1 day ahead. Store airtight at room temperature.
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