Boil carrots in water until carrots soften and are thoroughly cooked. Bring 1/2 cup of lentils to boil in 2 cups of water, cook lentils until they are cooked. Add water if necessary. Reserve water from both cooking the carrots and lentils.
When carrots and lentils are cooked, let them cool. When they are cooled, add carrots in 2 batches to blender. Add first batch of carrots plus 1/4 cup of reserved water from cooking carrots. You can also use regular water. Blend until carrots reach puree consistency. Do the same with the second batch of carrots. Put pureed carrots in a large pan.
Add cooked lentils to the blender along with 1/2 cup of reserved water from cooking lentils. Blend until pureed. Add pureed lentils to pureed carrots in a pan. Add 1/2 cup half-and-half. Heat through without boiling. Add all spices, stirring constantly. Add at least 1/2 teaspoon Cajun spice. Taste to check the flavor. Add salt and pepper, adjust other spices if necessary, going especially generous with Cajun spice.
Before serving, toast sliced almonds in the oven preheated to 350 F for about 5 minutes. Ladle soup in soup bowls. Sprinkle with toasted sliced almonds on top. Grind black pepper over the soup.