To a medium saucepan, add the chicken stock, ¾ cup (180 ml) water, sugar, tomato paste, ketchup, garlic, and sage. Set the heat to medium-high and bring to a boil. Once boiling, immediately reduce heat to low and simmer for 12-15 minutes, or until slightly reduced. Add the navy beans, and simmer for another 5 minutes. Separately, in a small bowl, whisk together the cornstarch and 1.5 Tbsp (21g) water to create a slurry. Gradually add half of the cornstarch slurry to the beans, whisking constantly to incorporate. If the desired thick consistency is reached, remove from the heat and enjoy. If not, add the rest of the cornstarch mixture and whisk to incorporate until thickened. Season, to taste, with salt and pepper and set aside.
In a large skillet, add unsalted butter and a generous glug of oil. Set over medium-high heat and melt until the butter starts bubbling. Add the mushrooms to one side of the skillet, cap side-down. Add the vine clusters of tomatoes to the remaining side of the skillet. Season to taste with salt. Nestle in a few sprigs of thyme, if desired. Cook for 3 minutes, untouched, until the mushrooms achieve a nice color. Carefully flip all of the mushrooms and cook for another 3 minutes until the tomatoes are soft and caramelized. Remove from the heat and set aside.
Heat a medium skillet over medium-high and coat the bottom with oil. Once the pan is ripping hot, add the back bacon and sear for 1-2 minutes. Flip and repeat on the other side. Remove the bacon from the pan. In the same pan, add in the sausages and sear on all sides for a total of about 5 minutes, until deep brown with a touch of char in spots.
Heat a medium nonstick skillet over medium-high heat. Add the butter to fully melt. Gently crack the eggs into the pan, being careful not to break the yolks. Let them cook just until the whites are set. Using a spoon, baste the tops of the eggs with the melted butter to both flavor and cook the whites, keeping the yolks runny. Remove from the pan onto a serving plate. Season with flaky sea salt and black pepper.
To a plate add the eggs seasoned with flaky sea salt, black pepper and a garnish of chopped fresh chives. Add a generous helping of English baked beans. Next add on the sausages and the cooked English back bacon. Spoon on the mushrooms and a few caramelized tomatoes. Serve with slices of toast, on the side (brioche, white, whole wheat, etc.).
