Prepare the Pudding:

1. Preheat your oven to 350°F (175°C).
2. Grease and line an 8×8-inch baking dish or a similar-sized pan.
3. In a food processor, pulse the pistachios until finely ground but not turned into a paste.
4. In a large bowl, whisk together the ground pistachios, flour, granulated sugar, light brown sugar, baking powder, baking soda, and salt.
5. In another bowl, mix the applesauce, plant-based milk, melted coconut oil, and vanilla extract.
6. Add the wet ingredients to the dry ingredients and stir until just combined.
7. Pour the batter into the prepared baking dish and spread evenly.

Bake:

1. Bake for 35-40 minutes, or until a toothpick inserted into the center comes out clean and the top is golden.
2. Allow the pudding to cool in the pan for 10 minutes.

Prepare the Honey Syrup:

1. While the pudding is baking, make the syrup.
2. In a small saucepan, combine the honey, water, lemon juice, and dairy-free butter.
3. Heat over medium heat, stirring until the butter is melted and the mixture comes to a boil.
4. Reduce heat and simmer for 2-3 minutes, stirring occasionally until slightly thickened.
5. Remove from heat.

Serve:

1. Once the pudding is slightly cooled, poke holes all over the top with a skewer or fork.
2. Pour the warm honey syrup over the pudding, allowing it to soak in.
3. Optionally, sprinkle with chopped pistachios.
4. Serve warm with a dollop of dairy-free whipped cream or a scoop of vanilla ice cream.