Two separate faults that compound. Together they were the cause of the bitterness in mixed-bone demi-glace batch 1.
The germ
The germ is the pale green shoot running through the centre of the clove. French practice is to degerm — degermer — and it is not fussiness.
The germ carries a higher concentration of the bitter precursors than the surrounding clove flesh, and that concentration rises as the bulb ages and the shoot develops. In a young, tight bulb the germ is barely present and can be ignored. Once it is visibly green and separable, take it out.
How. Split the clove lengthways with the flat of a knife and flick the shoot out with the tip. Takes a second per clove.
When it matters most. Anything where garlic is cooked long or hot, anything reduced, and anything raw in quantity — aioli, a raw dressing, a paste. In a quick sauté with a few cloves the difference is marginal.
The roasting window
Garlic goes from sweet to acrid over a narrow window, and it does so far faster than bones brown.
Intact garlic holds alliin and the enzyme alliinase in separate compartments. Cutting the clove breaks that separation and alliinase converts alliin to allicin. Allicin is unstable under heat and degrades onward to diallyl disulfide, diallyl trisulfide and related sulphur compounds. At moderate heat and short exposure this reads as sweet and roasted. Under sustained high heat the cysteine sulphoxides react further into sulphur heterocycles, which read as harshly bitter rather than pleasantly roasted.
Unlike an onion, garlic has very little free sugar to caramelise and carry the flavour in a sweet direction. There is nothing to balance the sulphur chemistry. It just goes bitter.
Batch 1 error. A halved head sat cut-face down on hot metal at 210 C for about 30 minutes, through the aromatics stage and the tomato paste pince. That is roughly three times too long.
Rule. For a stock or any long extraction, put garlic into the pot raw or barely coloured. If it goes on the roasting tray at all, give it the last 10 minutes and no more. It will still give up everything it has during hours of extraction.
Why this is expensive to get wrong
The resulting compounds are thermally stable. They formed at 210 C and are untroubled by anything that happens at 100 C afterwards. No reaction unmakes them. In a stock destined for reduction the error then concentrates by a factor of ten alongside everything else.
They are substantially lipophilic, however, which means lifting the fat cap after chilling removes a real fraction of them. That is the first move if it happens.