Apple Gel:

1. Peel and cut the apples into pieces.
2. In a saucepan, heat the apple pieces with water and sugar. Let it simmer for 15 minutes.
3. Blend everything into a smooth purée.
4. In a small bowl, mix the agar-agar with a bit of sugar.
5. Add this mixture to the apple purée and heat gently for 2 minutes.
6. Add lemon juice and let it cool. Then, pour the purée into a small dish to form a layer of jelly. Blend until you get a smooth gel.

Rich Gruyère AOP Ice Cream:

1. In a saucepan, heat the cream and milk without boiling.
2. In a bowl, whisk the egg yolk with sugar until frothy.
3. Gradually pour the warm milk into the egg-sugar mixture while whisking, then return everything to the saucepan.
4. Heat over low heat while stirring until the custard thickens.
5. Remove from heat and stir in the grated Gruyère AOP until it melts and incorporates into the cream.
6. Let the mixture cool, then place it in an ice cream maker and churn until it becomes ice cream.

Onion Compote:

1. Peel and finely slice the onions.
2. Melt the butter in a pan over medium heat, then add the onions. Cook gently, stirring regularly, for about 20 minutes until they become translucent.
3. Add the sugar and balsamic vinegar, then cook for another 10 minutes until everything is well caramelized.
4. Remove the thyme sprig and keep the compote warm.

Burnt Bread Foam:

1. Cut the bread into small pieces and lightly toast them in a pan until blackened and crispy.
2. In a saucepan, heat the milk and cream. Add the toasted bread pieces and let them infuse for 15 minutes.
3. Strain the mixture to remove the bread pieces.
4. Pour the liquid into a siphon and charge it with two gas cartridges.
5. Shake well and refrigerate for at least an hour.
6. When ready to serve, shake again and dispense the burnt bread foam directly onto the dish.

Final Plating:

1. Bottom of the Bowl: Onion Compote:
   Start by placing a generous spoonful of caramelized onion compote at the bottom of the wooden bowl. This soft and slightly sweet base will add depth of flavor. Ensure it occupies the center of the bowl, forming a thick layer, but not too compact, to allow space for the other elements.
2. Rich Gruyère AOP Ice Cream:
   Using a small spoon or quenelle, delicately place a portion of the rich Gruyère AOP ice cream on top of the onion compote. The ice cream should be creamy and melt slightly when it comes into contact with the other ingredients, adding a creamy touch and a pleasant contrast with the sweet-savory onion flavors.
3. Burnt Bread Foam:
   Next, with the burnt bread foam, form an airy cloud over the Gruyère ice cream. This will add a smoky dimension and a light, airy texture to the dish, contrasting pleasantly with the creamy consistency of the ice cream and the sweetness of the onion.
4. Country Bread Tuile:
   Gently place a crispy country bread tuile on top. The tuile adds crunch.
5. Apple Gel:
   Add apple gel directly onto the country bread tuile. The fresh, fruity apple gel will bring a refreshing note and an acidic contrast that balances the other flavors.
6. Caramelized Gruyère AOP Slices:
   For an added visual and gustatory effect, place a few slices of caramelized Gruyère AOP on top or around the dish.
7. Thin Granny Smith Apple Slices:
   Finally, place a few thin, clean slices of Granny Smith apple, spreading them around the dish or on top of the burnt bread foam.