Wash the fennel well. Cut off the tough parts of the fennel and the fronds and set them aside. Don't toss!
Keep one whole fennel for the salad and cut the other into 8 pieces.
Roast the fennel
Heat 1/4 cup olive oil in a heavy skillet. Add the fennel slices, season with salt and pepper, and sear them in a pan with the crushed garlic clove until nicely caramelized, turning as needed.
Deglaze with white wine and sweet soy sauce, let it reduce to a syrupy texture, then set the sauce aside.
Put the fennel on a baking tray, cover with foil, and bake at 350°F for 45 minutes.
Uncover, flip the pieces, and broil for 5 minutes to get a nice color.
Make the ajo blanco
Blend the fennel trimmings with 1/4 cup olive oil, white vinegar, garlic, stale bread, almonds, tahini, salt, and a bit of water. You want the texture to mimic a thick but pourable soup.
Strain through a fine sieve or chinois for a smooth texture.
Prepare the crunchy salad
Thinly slice the raw fennel using a mandoline or sharp knife, season with 2 tablespoons olive oil and lemon juice, salt, and pepper.
Add finely sliced spring onion and finely chopped green chili.
Plating
Pour the ajo blanco into a shallow bowl.
Place the fennel salad on top.
Add the golden roasted fennel pieces.
Finish with a drizzle of olive oil, a pinch of fleur de sel, and a spoonful of the reduced sauce.