Make béchamel: Heat butter in a 2-quart heavy saucepan over moderately low heat until melted, then add flour and cook roux over low heat, whisking, 3 minutes. Add hot milk in a fast stream, whisking vigorously, and whisk in garlic and salt. Bring to a boil, whisking. Reduce heat and simmer, whisking occasionally, 10 minutes, then remove garlic and add pepper.
Make mushroom tomato sauce: Pour boiling-hot water over porcini in a bowl and let stand until softened, about 20 minutes.Lift out porcini, squeezing excess liquid back into bowl, then rinse to remove any grit. Pour soaking liquid through a sieve lined with a dampened paper towel into another bowl. Chop porcini and add to soaking liquid.
Cook onion in oil in a 12-inch heavy skillet over moderate heat, stirring occasionally, until softened, 4 to 5 minutes, then stir in tomatoes with juice, sugar, porcini with soaking liquid, and 1 tablespoon basil. Simmer, stirring frequently, until tomatoes have broken down into a chunky sauce, about 25 minutes. Stir in salt and remaining tablespoon basil.
Assemble and bake lasagne: Cook lasagne noodles in a 6- to 8-quart pot of boiling salted water 8 minutes (noodles will not be cooked through), then drain and transfer to a bowl of cold water.
Put oven rack in middle position and preheat oven to 425°F.
Spread 1 cup béchamel on bottom of a buttered 13- by 9-inch baking dish, reserving remainder for last layer. Drain 3 lasagne noodles in 1 layer on a kitchen towel and arrange over béchamel in baking dish. Spread pasta in dish evenly with one third of mushroom tomato sauce and sprinkle with 1/3 cup cheese. Repeat layering of pasta, mushroom tomato sauce, and cheese twice, then cover with last 3 lasagne noodles. Spread remaining béchamel on top and sprinkle with remaining 3/4 cup cheese.
Bake, uncovered, until lasagne is bubbling and top is browned, 30 to 35 minutes. Let stand at room temperature at least 15 minutes before cutting.
Cooks' notes: · Béchamel and mushroom tomato sauces can be made 2 days ahead and cooled, uncovered, then chilled separately, covered. Bring sauces to room temperature before using. · You can assemble lasagne 1 day ahead and chill, covered. Bring to room temperature before baking.

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Nutrition Facts

Per Serving Per 100 g

Amount Per 1 Serving
Calories	176.93 Kcal (741 kJ)
Calories from fat	89.15 Kcal
		% Daily Value*
Total Fat	9.91g	15%
Cholesterol	19.49mg	6%
Sodium	344.24mg	14%
Potassium	201.48mg	4%
Total Carbs	12.79g	4%
Sugars	5.04g	20%
Dietary Fiber	1.01g	4%
Protein	8.81g	18%
Vitamin C	7.5mg	12%
Calcium	87.9mg	9%

Amount Per 100 g
Calories	102.45 Kcal (429 kJ)
Calories from fat	51.62 Kcal
		% Daily Value*
Total Fat	5.74g	15%
Cholesterol	11.28mg	6%
Sodium	199.33mg	14%
Potassium	116.66mg	4%
Total Carbs	7.4g	4%
Sugars	2.92g	20%
Dietary Fiber	0.59g	4%
Protein	5.1g	18%
Vitamin C	4.3mg	12%
Calcium	50.9mg	9%

* Percent Daily Values are based on a 2000 calorie diet. Your daily values may be higher or lower depending on your calorie needs.
Find out how many calories should you eat.

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