In a small saucepan, heat the milk over medium heat until it’s warm but not simmering (about 95 degrees F), about 1-2 minutes. Add the cubed 3 tbsp butter to the pan, turn heat down to low, and stir gently until the butter has melted into milk. Remove from heat and let cool 5 minutes.
While the milk mixture cools, whisk together the yeast, sugar, flour, salt, 3 tsp caraway seeds, and 1 tbsp fresh thyme leaves in a large bowl.
Temper the eggs by whisking some cooled milk mixture into the eggs, one tablespoon at a time. After 4-5 tablespoons, whisk the tempered eggs into the saucepan with the remaining warm milk.
Pour the egg and milk mixture into the dry ingredients. Mix together at first with a spatula, but once the ingredients are mostly combined together, use your (clean!!) hands to form a soft, sticky dough.
Leave the dough in the bowl and cover with plastic wrap. Set dough to rise in a warm place for 2.5 hours, or until doubled in size.
Once the dough has risen: lightly dust your worksurface with flour, then spray a 9x9 baking dish with cooking spray. You might want to spritz a little cooking spray on your hands, too, since the dough will be sticky.
Remove dough from the bowl and place on your floured work surface. Shape dough gently into a disc and then use a sharp knife or bench scraper to divide the dough into 9 (roughly) equal pieces.
Quickly and lightly roll each piece of dough into a ball and place in the greased baking dish. You should have three rows of three biscuits each, spaced out so none are touching.
Cover the baking dish with plastic wrap and let rise for a second time until biscuits are doubled in size and are now touching each other, about 45 minutes.