Make the filling: Preheat oven to 375 degrees. In a saucepan over medium-high heat, combine dates with 1½ cups water and bring to a boil. Reduce to a simmer for 2 minutes, then remove from heat. Stir in baking soda, then set aside.
In the bowl of a stand mixer fitted with paddle attachment, cream butter and sugar together on high speed until fluffy. With mixer on low, add eggs one at a time, then add vanilla. Slowly incorporate flour and salt, followed by dates and cooking liquid. Once well-combined, stir in baking powder by hand. Pour batter into pie crust and bake for 40 minutes.
Make the glaze: In a medium saucepan, combine butter, brown sugar, cream, and salt. Bring to a boil, then reduce to a simmer for 1 minute. Remove from heat and stir in rum. Set aside.
Using a fork, poke holes all over pie. While glaze is still warm, pour ¾ over pie and allow to absorb for 30 minutes. Reserve remaining glaze and reheat just before serving. Drizzle warm glaze over each slice of pie.