In a medium saucepan over high heat, bring the water, salt, and bay leaf to a boil. Add the carrots, lower the heat, and simmer for 3 minutes. Add the potatoes and simmer for an additional 10 minutes, until both vegetables are soft. Drain, reserving the liquid and discarding the bay leaf. Set aside.

In a large sauté pan set over high heat, melt the butter, add the country ham, and sauté until golden on the edges, about 3 minutes. Add the onion and continue to sauté another minute. In a small bowl, dissolve the cornstarch in ½ cup of the reserved cooking liquid, then whisk it into the country ham mixture along with the thyme, garlic, and chili sauce. Continue to simmer, whisking until the sauce is lightly thickened. Add the potatoes and carrots and simmer to reheat. Thin with additional cooking liquid if necessary to make a light thin sauce coating the vegetables.