1. Make the dough: In the bowl of a stand mixer fitted with paddle attachment, combine yeast, 2 cups milk, sugar, salt, eggs, and 6 cups flour. Mix ingredients on low speed until they form a ball, about 1 minute. Increasing the speed to medium-low, slowly add butter, one pat at a time, until incorporated.
2. Using the dough hook attachment, knead on medium-low speed for 5 minutes. The dough should be soft and supple, not sticky—adjust with additional flour or milk if necessary. Continue kneading for 2 minutes more. Remove a small piece of dough. It should stretch enough that you can see through it before it tears. If you can’t, continue kneading until the dough passes this test.
3. Remove dough and place into a lightly oiled bowl and cover with plastic wrap. Let sit at room temperature until it doubles in size, about an hour.
4. Turn dough onto a lightly floured work surface and divide it into 36 pieces that are about 1½ ounces each. Moving the palm of your hand in tight circular motions, shape the dough into small balls.
5. On two greased baking trays, place balls about an inch apart from one another, brush with melted butter, and cover loosely with plastic wrap. Allow to double in size.
6. Meanwhile, make the filling: In a nonreactive pot or dutch oven over high heat, combine figs, sugar, salt, and water. Bring mixture to a simmer then reduce heat to medium. Stirring frequently, reduce mixture until it is thick and syrupy and the figs are completely tender, about 20 minutes (this may take longer depending on ripeness of figs). Stir in lemon juice and zest. Cool and refrigerate. If making ahead of time, mixture will keep 5 days in refrigerator.
7. After dough balls have doubled in size, use your fingers to create a pocket, pulling outward from the center of each ball. Be gentle to avoid degassing the dough.
8. Spoon about 1½ ounces of filling into each dough ball and top with 1 tablespoon ricotta. Brush with melted butter and cover loosely with plastic. Preheat oven to 400 degrees.
9. Kolaches are ready to bake when they have doubled in size and look light and puffy, about 45 minutes after filling depending on room temperature. Brush them with more melted butter, then place trays in oven and bake for 20 minutes. Rotate pans and bake for 10 minutes more. The dough should be golden brown and between 190 and 200 degrees. Remove from oven and use a fork to drizzle a light stream of honey over top. Let cool slightly before serving.