In food processor, pulse carrot until broken into rough 1/4-inch pieces, about five 1-second pulses. Add celery and onion; pulse until all vegetables are broken into 1/8-inch pieces, about five 1-second pulses.
Heat butter in large heavy-bottomed saucepan over medium-high heat; when foaming subsides, add vegetables and cook, stirring frequently, until softened and WELL BROWNED, about 7 minutes (important step: browning will give the gravy great flavor). Reduce heat to medium; stir in flour and cook, stirring constantly, until THOROUGHLY BROWNED and fragrant, about 5 minutes (again the browning is very important step for flavor). Whisking constantly, gradually add broths; bring to boil, skimming off any foam that forms on surface. Reduce heat to medium-low and add bay leaf, thyme, and peppercorns; simmer, stirring occasionally, until thickened and reduced to 3 cups, 20 to 25 minutes.
Strain gravy through fine-mesh strainer into clean saucepan, pressing on solids to extract as much liquid as possible; discard solids. Adjust seasonings with salt and pepper. Serve hot.
NOTE: If you would like to double the recipe, use a Dutch oven to give the vegetables ample space for browning and increase the cooking times by roughly 50 percent. The finished gravy can be frozen. To thaw either a single or double recipe, place the gravy and 1 tablespoon of water in a saucepan over low heat and bring slowly to a simmer. The gravy may appear broken or curdled as it thaws, but a vigorous whisking will recombine it.