Trim off each endive bottom and remove one or 2 outer leaves. Soak outer leaves first and endives in lemony water and drain well. Chop outer leaves. Heat up a large saucepan or dutch oven, melt butter, throw in garlic and the chopped endive leaves, season with salt and pepper and sweat for about 4 min. Add heavy cream, bring to boil and let simmer for 45 min to reduce; uncovered. Pass through a sieve. Save solids if desired and reserve the reduced endive flavored cream.
In a large skillet, melt 2 tablespoons/30g butter and glaze endives. Add chicken stock, season with salt, and bring to a boil. Cover and let simmer for 30 minutes or until fork tender. Drain endives well and let cool – squeeze out excess moisture left inside each endive and reserve on paper towels. Save stock for later use.
In a heated frying pan, melt butter and sprinkle sugar. Arrange cooked endives and lightly caramelize on both sides – let cool.
Wrap each endive in ham, arrange them in a shallow dish, glaze with the reduced cream sauce, and cheese. Place under the broiler to slightly brown. Bon appétit!