Add the warm water, warm milk, melted butter, eggs, instant yeast, and sugar to the bowl of a stand mixer. Use a fork to stir briefly until combined.
Add 6 cups (720 g) of the bread flour, the everything bagel seasoning, and the kosher salt. Attach the dough hook and mix on low speed until the dough begins to come together around the hook. If the dough does not pull away from the sides of the bowl, add additional flour 2 to 3 tablespoons at a time, mixing between additions, until a soft, slightly tacky dough forms. The dough should feel supple and elastic, not sticky or dry. Continue kneading for 4 to 5 minutes after the dough clears the bowl to properly develop the gluten, which is key to achieving the desired chewy texture.
Remove the dough briefly from the bowl. Lightly spray the bowl with nonstick cooking spray, return the dough to the bowl, and cover tightly with plastic wrap. Let the dough rise in a warm, draft-free place until doubled in size, about 1 hour.
Line a rimmed baking sheet with parchment paper and set aside.
Turn the risen dough out onto a clean work surface. Divide the dough into 18 equal pieces by first dividing it in half, then dividing each half into thirds, and dividing each third into thirds again. Roll each piece into a smooth ball and arrange them evenly on the prepared baking sheet in a 6-by-3 layout.
Cover the rolls lightly with greased plastic wrap and let them rise again until nearly doubled in size, about 30 to 45 minutes. During the second rise, preheat the oven to 350°F (177°C).
In a small bowl, whisk together the egg and milk to make the egg wash. Gently brush the tops of the risen rolls with the egg wash, then sprinkle generously with everything bagel seasoning so it adheres evenly.
Bake for 18 to 23 minutes, or until the rolls are golden brown on top and baked through on the bottom. Remove from the oven and transfer to a wire rack to cool slightly.
Serve warm, optionally with cream cheese.