In the bowl of a stand mixer, place the cheese and milk. (Or use a medium-sized bowl and a wooden spoon.) Using the paddle attachment, whip the cheese (or stir it vigorously) for at least 5 minutes, or until it is very smooth and creamy. If the cheese is still crumbly, add more milk 1/2 teaspoon at a time.
To assemble, spread about 1/8 teaspoon of cheese on each apricot. (If using California apricots, put the goat cheese on the shiny side.) Drizzle a little honey over the cheese and top with a light sprinkling of thyme. Place a walnut half on top, arrange the apricots on a platter and serve.