In a measuring cup, pour yeast over the top of the milk. Add the sugar and stir the contents together. Set aside for about 10 minutes to allow the yeast to bloom. The surface should become foamy.
Into the bowl of stand mixer, pour 2 cups of flour, rosemary and kosher salt. Use a fork or whisk to evenly disperse the ingredients throughout the flour.
Add the bloomed yeast/milk mixture to the mixing bowl along with the olive oil. Using the dough hook attachment, mix it on low speed for 15-20 seconds.
Add 2 eggs. Beat on low for 30 seconds, scrape down the sides and beat on medium for about 3 minutes.
Add the remaining 2 cups of flour, 1 cup at time. Beat just until each cup is incorporated and scrape down the sides in between. The dough should pull away from the sides of the bowl, but still be a little sticky.
Dust a work surface with the remaining 2 Tbsp of flour and turn your dough out. Knead by hand for 3 to 5 minutes, incorporating all the flour.
Shape it into a ball and place it in a lightly greased bowl. Turn it over once to coat, cover and set in a warm, dry spot for about 1 hour. It will double in size.
Meanwhile, make the poppyseed honey butter. Add butter, milk, honey and salt to a medium mixing bowl (to contain splatter). Whip them together with a hand mixer, first on low speed to combine, then on high speed for 3 to 4 minutes. Mix in the poppyseeds on low speed for a few seconds to distribute them throughout. Cover and refrigerate until half and hour before serving.
Punch down the dough. Lightly dust a work surface with flour. Turn out the dough and divide into 12 equal parts. Shape each into a ball by pulling the edges under smoothing out the top. Place the rolls, evenly spaced, onto a lightly greased 9"x13" baking pan. Cover them and allow to rest for 45 minutes. They will double in size again.
Preheat the oven to 350 degrees. After the rolls have rested, bake them for 20 to 23 minutes. Remove them to a cooling rack.
Transfer to a basket and serve alongside Poppy Seed Honey Butter.