Savoury version of caramel or sugar cage

You can make some pretty delicate cages using pastry, which is (or can be) pretty neutral in flavor.

An example is posted on a foodie blog post about a dinner they had at the restaurant L'Heritage in Kuala Lampur.

Slow-braised Black Angus ribs with sweetbread & morels in a choux pastry cage.

Images for "choux pastry cage" are pretty easy to find and they seem to be made in a couple of ways:

• A "lattice" style cage that uses flat (premade) puff pastry dough into which slits are cut and then stretched to create openings and then baked. This can be done by hand or with a specialty rotary cutter called a "lattice cutter". Described in detail in this Joepastry article.
• Using choux pastry, pipe the pastry around a form in the pattern you like using a small tip and then bake. This is described in a YouTube video here.

Joe Pastry's beautiful caged pears using the lattice cutter look like this:

The choux pastry from the video comes out looking like this... he uses them as bowls but you should be able to use them as cages instead.

I wonder if you could modify a recipe for cheese crisps.

The recipes I'm familiar with involve heating cheese through the melted stage and to a crispy crusty stage. It's usually done in disks or puddles, though the appearance is often airy or holed - from the bubbling of the cheese as it dries and sets, much like the lacy, caramelized cookies (Florentine, I believe).

And it seems from the recipes that it takes a bit for the cheese to crisp up after being taken off the heat, so you may be able to drape or fold the cheese directly from the heat so that as it cools it sets, crisps up, in rounded or arching configurations... and if you can't, you might be able to crisp them in such configurations using curved metal surfaces, like a metal or oven-safe glass bowl.

To move from the bubbly lacy disks to something more airy and cage-like, you would want long shreds - the cheese should be cut to matchsticks, rather than grated. Pre-shredded cheese is often dusted with starch which might help the shreds dry out by providing binding to the escaping oils... though it's probably not difficult to dust your own matchsticks if it does, in fact, help.

You'd have to scatter the shreds quite loosely to prevent them melting together - that is, with enough gaps to leave an impression of a net or cage. Because the space between means each strand or tangle is cooking more or less on their own on the baking sheet, you would need very short cooking times and a lot of vigilance to catch them while crisp and before burnt.

I think your question is more about the savoriness, as opposed to the technique of making the tuile. If so, look into less sweet sugars as a base, perhaps isomalt or an isomalt glucose mix.