Step 1

If adding powdered gelatin to chicken stock, pour stock into a measuring cup or medium bowl and sprinkle gelatin all over the surface. Let stand.

Step 2

In a 3-quart saucier or saucepan, cook bacon over medium-high heat, stirring occasionally, until browned and starting to crisp, about 5 minutes. Using a slotted spoon, transfer bacon to a plate, leaving rendered bacon fat in the saucier.

Step 3

Add diced mushroom caps and cook, stirring, until they release their water and then brown all over, about 6 minutes; add oil as needed at any point if saucepan becomes too dry. Season with salt and pepper. Scrape sautéed mushrooms onto plate with bacon and set aside.

Step 4

Add small diced carrot and pearl onions to the saucier, and cook, stirring, until just softened, about 5 minutes; add oil at any point if the pan becomes too dry. Transfer carrots and pearl onions to plate with bacon and mushrooms.

Step 5

Add reserved mushroom stems, large diced carrots, shallots, 1 clove garlic, and thyme sprig to saucier and cook, stirring, until just starting to brown; lower heat and/or add oil to saucier at any point to prevent scorching. Add red wine and bring to a simmer, scraping up any browned bits from bottom of the pan. Continue to simmer until wine is reduced by half.

Step 6

Meanwhile, mix butter with flour until thoroughly incorporated; keep cool.

Step 7

Add chicken stock and gelatin to saucier and return to a simmer. Continue cooking until reduced by one third. Strain sauce into a heatproof bowl, discard solids, then return to the saucier. Whisk in butter-flour mixture, then simmer until sauce begins to thicken and coats the back of a spoon, about 3 minutes. If sauce is thin, you can reduce further, or whisk in additional butter-flour mixture. Season with salt and pepper. If it tastes too sharp or acidic, you can whisk in a pinch of sugar to round out the flavor.

Step 8

Add bacon and vegetable garnishes to the sauce and heat through. Rub toasts with remaining clove of garlic, then set on serving plates. Slide 2 poached eggs onto each toast. Spoon the sauce and garnishes all over, sprinkle with parsley, and serve right away.