Combine 1 cup of the flour, yeast, sugar and salt in a large bowl.
Heat milk and butter until very warm (120 to 130 degrees F).
Add to flour and mix until well blended, about 1 minute. Gradually add enough remaining flour (3/4 to 1 ¼ cups) to make s soft dough. Dough should form a ball and will be slightly sticky. Knead on a floured surface or in the bowl of stand mixer with dough hook until smooth and elastic, about 4 minutes. (If using Rapid
Rise yeast, let dough rest at this point for 10 minutes.)Pat dough with floured hands to fill greased pizza pan or baking sheet. I patted the dough into a 12 inch circle directly on a large (12 to 16 inch) pizza dish. Form rim. Cover with a towel and let rest 10 minutes.For topping, mix flour, brown sugar, cinnamon and nutmeg in a bowl – I used the same bowl I’d used for the pizza dough.
Cut in butter with pastry blender or two forks until crumbly. Stir in oats.
Sprinkle over pizza crust.
Sprinkle walnuts over top.
Bake on lowest oven rack for 12 to 15 minutes, until topping and crust are browned.
Remove from oven and let cool on wire rack for 5 minutes.To make the icing, melt the butter in a 2 cup glass microwave-safe measuring cup.
Add the sugar and stir (it will still be thick and powdery at this point), then add milk 2 teaspoons at a time until it is the consistency of glue or slightly thicker.
Add the vanilla.
Transfer to an unsnipped decorating bag (no tip required) or a heavy duty freeze bag. Snip the tip or corner of the bag and drizzle over the pizza before serving.
