Pour the flour into the bowl of a stand mixer and add the salt and yeast on opposite sides, then stir each one in with your finger.  This prevents the salt from touching the yeast directly, which can kill it.

Add the vegan butter, brown sugar, pumpkin spice, and pumpkin puree and mix on medium-low speed with the paddle attachment until the mixture is crumbly.

Keep the mixer on as you trickle in the almond milk.  Let the mixer blend the ingredients to create a slightly sticky dough.  Continue to add more milk as needed; there should be no flour at the bottom of the bowl.

Switch attachments to the dough hook.  Turn the mixer on medium-low speed and let it knead for about 7 minutes, or until the dough is smooth, less sticky, and passes the windowpane test.  This means that a lump of dough can be stretched until it's translucent without tearing.  If it doesn't pass the windowpane test, knead for another minute and check again.

Shape it into a ball and place it back into the mixing bowl.  Cover it with plastic wrap and set it in a warm place to rise until doubled in size, about 1 to 1 ½ hours.

Measure out the filling and frosting ingredients while the dough is rising.

Once it has doubled in size, scrape it out onto a floured surface and punch it down all over to knock out any pockets of gas.

Use a rolling pin to roll it out into a square, measuring about 19x19 inches.  The dough should be fairly thin, but keep in mind that it will expand as it rises a second time.

Roll it up tightly from one end, then pinch the seam to form a log.  Cut the log into 12 equal pieces using a piece of thread or dental floss.  Do this by wrapping the thread around the log and cinching it tighter and tighter, like a noose, until the log is cut.

As soon as the baked rolls come out of the oven, spread the frosting on top with an angled spatula or butter knife.  Let them cool for 15 minutes before serving.