*If you don't have rapid or quick-rising yeast and need to use regular instant yeast (such as SAF) or Active Dry yeast, proof yeast in 1/4 cup lukewarm water. Mix remaining 1/4 cup water with the 1/4 cup milk and butter and heat as prescribed. Add all to the dough. PLUS* replace the 10-minute dough rest with a full first rise to doubled, probably 30-45 minutes.
Combine 2 cups of the all purpose flour, salt and quick-rising yeast in a large bowl or the bowl of your stand mixer, fitted with the kneading hook. In a small saucepan or in the microwave, heat the water, milk and 2 Tbsp. butter until just warm to the touch (about 105F). Stir in the maple syrup.
Stir the milk mixture into the dry ingredients, then add egg and mix in until well combined, scraping down the bowl as needed to combine the flour. Start adding more flour, in small increments, mixing in well before adding more. Continue adding flour until you have a moist dough that wraps around the hook and cleans the bowl of the mixer. Remove dough to a lightly floured surface and knead briefly. Form into a ball, cover with a clean tea towel and let rest 10 minutes.
Meanwhile, prepare the filling. Add the chopped walnuts to a food processor and pulse a few times to break them down a bit. Add the brown sugar and butter and pulse a few times until you have an even crumb mixture. Add the maple syrup and pulse in once or twice. Set aside.
Prepare the pan by greasing an 8x8-inch baking pan well with butter, oil or cooking spray. Pour the maple syrup into the pan and tilt to spread evenly over the bottom of the pan. Sprinkle the brown sugar evenly over-top. Scatter the walnuts evenly over-top, as well. Dot the diced butter over the top. Set aside.
(Refer to the Step-by-Step Photos above the Recipe Card if you are unsure about this rolling and cutting process). Remove dough to a lightly floured work surface and deflate. Roll into a rectangle 9-inches wide and about 14-15 inches long. Scatter prepared filling over-top of the dough and spread out evenly right out to the edges. Starting from the short (9") end, roll up jelly-roll style. Use a measuring tape or stick to adjust the loaf to exactly 9-inches wide (press in from the ends of the roll). Measure out nine 1-inch slices using a measuring tape and cut the log into slices. Place the slices, cut side up, on top of the maple syrup/walnut mixture in the pan. Cover the pan with plastic wrap and set to rise until doubled, about 40-45 minutes.
Preheat oven to 350F.
When buns are risen, remove the plastic wrap and place the baking pan on top of a baking sheet (to catch any bubble-overs!). Place into preheated oven and bake for 35-40 minutes, or until golden and they sound hollow when tapped. *Check buns at about the 30 minute mark and if they are already browned sufficiently, loosely cover the top with a sheet of aluminum foil for the last part of baking.
Remove from oven. Run a knife around the outside of the pan very thoroughly, to ensure there is no sticking on the sides of the pan. Also, if some of the centres of the buns have popped up during baking, use the side a knife to gently press them back down where they belong. Cover a baking sheet with a piece of parchment paper, then invert the hot buns on top of the parchment. If they don't immediately fall out, tap on the bottom of the pan with the butt of a knife until they do.
Allow buns to cool to at just warm or cool completely before eating.
These buns will keep several days at room temperature in an air-tight container. They will also freeze well.
Be sure to read the Ingredient and Cook's Notes above this Recipe Card. You will also find Step-by-Step photos there, for reference, if you are unsure about any part of the instructions.