In a medium saucepan, combine 2 cups of heavy cream, 1 cup of whole milk, 3/4 cup of brown sugar, 1/2 teaspoon of ground cinnamon, 1/4 teaspoon of ground ginger, 1/4 teaspoon of ground nutmeg, and 1/4 teaspoon of salt. Heat over medium heat, stirring until warm and sugar dissolves (about 5-7 minutes). Avoid boiling.

In a separate bowl, whisk together 4 large egg yolks until slightly thickened. Gradually add 1/2 cup of warm cream mixture to temper the eggs, whisking constantly. Once combined, stir this back into the saucepan.

Cook the mixture on low heat, stirring frequently until it thickens enough to coat the back of a spoon (about 10-15 minutes). Ensure it reaches around 170°F before removing from heat.

Stir in 1 teaspoon of vanilla extract and 1 cup of finely grated, steamed carrots. Blend using an immersion blender until smooth and creamy.

Transfer to a bowl, cover with plastic wrap (touching the surface to avoid skin formation), and refrigerate for at least 4 hours or overnight to chill thoroughly.

Pour mixture into an ice cream maker and churn according to manufacturer's instructions (about 20-25 minutes) until soft-serve consistency. Optionally, add 1/2 cup of pecans or graham crackers in the last 5 minutes.

Transfer churned ice cream to a freezer-safe container, smoothing the top. Seal tightly and freeze for at least 4 hours until firm. Let sit at room temperature for 5-10 minutes before scooping to serve.