- Place large saucepot on low heat and gently melt butter. Add onions, lightly season with salt, and stir to combine. Simmer onions on low heat for 3 hours, constantly stirring until extremely soft. Cool onions to room temperature, about 20 minutes.
- Place onions in high-speed blender with kappa and iota carrageenan. Blend mixture on high speed until smooth and creamy.
- Line a ¼ sheet pan with a smooth single layer of plastic wrap. Add onion purée to a saucepot and simmer for 3 minutes. Pour onion purée on to the sheet pan, filling completely, forming a ¼-inch-thick layer. Place sheet pan in refrigerator and cool. The purée will gel to a pudding-like texture.
- Char bread slices on both sides over a charcoal grill. Cool and break into 1-inch pieces. Place into a blender and season with salt and black pepper. Blend bread on high until it is a breadcrumb consistency. Remove from blender and reserve.
- Meanwhile, peel apple, remove core, and cut into a micro brunoise. In a mixing bowl, mix apple and vinegar. Season with salt and combine.
- For plating, remove onion pudding from refrigerator.With a 3-inch ring mold,cut four rounds of pudding. Using a small spatula, gently place each round in the center of the plate. Garnish pudding with 1 tablespoon of apple and 1½ teaspoons trout roe, keeping garnish on top of the onion pudding and spreading evenly. Finish plate with 1 tablespoon burnt breadcrumbs and 5 chervil stems.
*Carrageen is a gelling and thickening agent extracted from red seaweed. It comes in powdered form and can be purchased at gourmet food stores or online at places such as modernistpantry.com.