Place warm water in the bowl of a stand mixer fitted with a dough hook OR a large bowl. Dissolve yeast in water and let stand 5 minutes until foamy.
Mix honey, egg, and melted butter into yeast mixture until smooth. Add salt and 3 cups flour to bowl and mix on low speed OR with a wooden spoon if making dough by hand until dough pulls away from sides of bowl, about 2 minutes of mixing (if dough seems a bit wet, add additional flour by the tablespoon until dough pulls away from sides of bowl)
If making dough in stand mixer, knead dough in mixer on low speed 5-7 minutes until dough is stretchy and elastic. If making dough by hand, turn dough onto a lightly floured surface and knead by hand until dough is stretchy and elastic, about 10 minutes of kneading.
Place dough in a greased bowl, turning once to grease top. Cover bowl with plastic wrap and let rise in a warm place at room temperature 1 to 1-1/2 hours until dough is doubled in size.
Grease a 9x15 loaf pan. Turn dough onto a floured surface and roll into a 9x15 inch rectangle. Scatter cubed cheddar over dough rectangle, tightly roll up dough, and pinch ends to seal. Cut dough in half vertically and tightly twist two halves together, tucking ends under. Transfer loaf to prepared pan.
Allow loaf to rise in a warm place at room temperature 30-45 minutes until loaf is puffy and nearly doubled in size.
Preheat oven to 375F. Brush risen loaf with egg wash and bake at 375F 30-35 minutes until loaf is golden brown and registers 180F in the center (cover bread with a sheet of tin foil if it browns too fast).