Heat 1 tsp oil in a heavy-bottomed, large saucepan.
Add the grated squash and salt. Saute about 10 minutes, stirring frequently. The mixture will exude a lot of liquid.
Add the almond milk, bring the mixture to a boil, reduce heat to medium-low so it boils gently, and let it cook about an hour to 90 minutes, or until the liquid has completely evaporated. Stir frequently while the mixture reduces. Don't be tempted to rush the process by using less liquid. You really need to let the liquid and heat infuse the squash over a period of time so it gets all silky and tender.
Add the sugar and vanilla extract and mix thoroughly. Turn off the heat.
In a small saucepan, heat the remaining 1 tsp of oil, add the chopped walnuts and cardamom, and saute for a minute or until the walnuts turn lightly golden.
Add to the halwa and mix thoroughly.
Halwa, to my mind, tastes best chilled. But if you just can't wait, allow it to cool slightly and attack. After that first bite, you'll be a new person.