Melt the bacon fat and butter in a medium saucepan over medium-high heat. When the bubbles subside, pour in the tomatoes and stir with a wooden spoon until the fat has married with the tomatoes. Reduce the heat to low and simmer, stirring regularly, until reduced by half, 2 hours.
Heat the evaporated milk and the whole milk in separate saucepans over low heat until they form a skin on the surface. Remove and discard the skin from the evaporated milk, then pour into the tomatoes; stir until incorporated.
Put the flour in a large mixing bowl. Remove and discard the skin from the whole milk. Quickly pour the milk into the bowl with the flour, whisking vigorously (to avoid clumps). Pour the mixture through a fine-mesh strainer into the pot with the tomatoes. Stir with a wooden spoon until incorporated. (The consistency should be velvety.) Season with 2 tablespoons each salt and pepper.
This recipe was provided by a chef, restaurant or culinary professional. It has not been tested for home use.