Preheat oven to 420 degrees F, and bring about 3 cups of water to a boil on the stovetop.
Spread the broccoli florets and peeled whole garlic cloves out on a parchment paper lined baking sheet. Drizzle with 2 tbsp of olive oil, and toss to coat. Bake for 18 minutes, then remove from the oven.
While the broccoli is baking, place the almonds in a bowl and pour boiling water over the top until they are fully submerged. Allow them to soak in the boiling water for 10 minutes. Drain the water and rinse with cold water so they are easy to handle.
Using your fingers, remove the skin of the almonds. This step should be very easy, and they should easily come out of their skin.
Place a large dutch oven or pot over medium heat. Drizzle in 1 tbsp of olive oil, and sautee the chopped onion until it begins to become translucent, about 5 minutes.
Add the roasted red chili paste to the pot and stir well for about 60 seconds before adding the vegetable broth, roasted broccoli, roasted garlic cloves, blanched almonds, 1/2 tsp salt, and 1/4 tsp pepper.
Bring to a simmer, cover, lower the heat to medium, and cook for 30 minutes, stirring occasionally.
When the soup is done simmering allow it to rest uncovered for 15-20 minutes before transferring the mixture to a high-speed blender. Blend until smooth (at least 60 seconds). You may choose to do this in batches.
At this point you will want to check the consistency and add more broth if you would like to thin it out.
Transfer the soup back to the dutch oven and heat over medium heat until warm. Add the lemon juice. Pour in the feta cheese and stir until melted. Taste test, and add salt as needed.
Ladle into bowls and serve with feta cheese and red pepper flakes sprinkled over the top. You can also serve it with a piece of crusty bread. Enjoy!