In a mixing bowl, combine the warm whole milk and honey, stirring until the honey is dissolved. Sprinkle the instant dry yeast over the milk mixture and let it sit for about 5-10 minutes until foamy.
Once the yeast is activated, add the beaten eggs and melted butter to the bowl. Mix well. Gradually add 3 cups of all-purpose flour and the kosher salt, stirring until a soft dough begins to form. If the dough is too sticky, add more flour, a little at a time, until it pulls away from the sides of the bowl.
Transfer the dough to a floured surface and knead it for about 5-7 minutes until smooth and elastic. Form the dough into a ball and place it in a lightly greased bowl. Cover with a kitchen towel and let it rise in a warm place for about 1 hour, or until it has doubled in size.
While the dough is rising, prepare the filling. In a separate bowl, combine the shredded cheddar cheese, fresh thyme, everything bagel spice, and crushed red pepper flakes. Mix until well combined.
Once the dough has risen, punch it down and transfer it to a floured surface. Roll it out into a rectangle, about 12x18 inches in size.
Spread the basil pesto evenly over the rolled-out dough, leaving a small border around the edges.
Sprinkle the cheddar cheese mixture evenly over the pesto-covered dough.
Starting from the long edge, carefully roll the dough into a tight log. Once rolled, slice the log into 12 equal pieces.
Place the sliced buns on a baking sheet lined with parchment paper, leaving space between each bun. Cover with a kitchen towel and let them rise for another 30 minutes.
Preheat your oven to 375°F (190°C). Once the buns have risen, bake them in the preheated oven for 20-25 minutes, or until golden brown on top.
Remove the buns from the oven and let them cool for a few minutes before serving. Enjoy them warm, straight from the oven, or at room temperature.
